Answer:
r = 3
Step-by-step explanation:
starting with
2 / r = 12 / 18. we cross multiply
18 * 2 = 12 * r
36 = 12 * r
and divide by 12 to isolate "r"
36 / 12 = r
Then r = 3
Which table shows a proportional relationship between x and y?
From the given tables, Tables 2 and 3 will show the proportional relationship between x and y.
What is Proportionality:Two ratios or two fractions are comparable according to the equation of proportion. In other words, when two ratios are equal, they are said to be proportionate.
Let x and y be proportional relation
=> x ∝ y
=> x = ky
=> x/y = k [ where 'k' proportionality constant ]
Here we have
Table 1
x 2 3 4 5
y 7 9 11 13
=> [tex]\frac{x}{y} = \frac{3}{7} = \frac{3}{9}[/tex] [ which is not true ]
Hence,
Table 1 not shows any proportional relationship between x and y
Table 2
x 3 7.5 15 25
y 1 2.5 4 6
=> [tex]\frac{x}{y} = \frac{3}{1} = \frac{7.5}{2.5} = 3[/tex] [ which is true ]
Hence, Table 2, shows a proportional relationship between x and y
Table 3
x 1 2 7 8
y 0.5 1 3.5 4
=> [tex]\frac{x}{y} = \frac{1}{0.5} = \frac{2}{1} = 2[/tex] [ Which is true ]
Hence, Table 3 shows a proportional relationship between x and y
Table 4
x 3 6 8 10
y 12 15 18 20
=> [tex]\frac{x}{y} = \frac{3}{12} = \frac{6}{15}[/tex] [ Which is not true ]
Hence, Table 4 not shows a proportional relationship between x and y
Therefore,
From the given tables, Tables 2 and 3 will show the proportional relationship between x and y.
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Darby has a $50 gift card to spend at a coffee shop. Each cup of coffee is $2.40. Write and solve an inequality to determine how many cups of coffee she can buy so she has at least $8 left to purchase an insulated mug.
Question: Darby has a $50 gift card to spend at a coffee shop. Each cup of coffee is $2.40. Write and solve an inequality to determine how many cups of coffee she can buy so she has at least $8 left to purchase an insulated mug.
To make an equation we need to do $50-$8 to see how much money we have left to spend on coffee after buying the mug which is $42
42 divided by 2.4 = 17.5 but since you cant buy half a coffee you’d get 17 with $1.2o left over
A way to write this equation is 2.4C + 8 = 50
C acts as a variable to represent the number of cups of coffee you can get while 8 just stands for the one insulated mug you want
hope this helps :D
Answer: 2.4C + 8 = 50
Use the figure to the right to find the value of PT. T is the midpoint of PQ.
PT=3x+6 and TQ=5x-6
The value of the variable 'x' is 6. Then the length of the line segment PT will be 24 units.
What is a line segment?A line segment in mathematics has two different points on it that define its boundaries. A line segment is sometimes referred to as a section of a path that joins two places.
The information is given below.
PT = 3x + 6 and TQ = 5x - 6
T is the midpoint of PQ. Then the equation is given as,
PT = TQ
3x + 6 = 5x - 6
2x = 12
x = 6
Then the length of the line segment PT will be given as,
PT = 3(6) + 6
PT = 18 + 6
PT = 24 units
The value of the variable 'x' is 6. Then the length of the line segment PT will be 24 units.
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.A certain store is selling packages of 10 pencils and 4 pens for back to school. The store manag wants to make a larger package in the same ratio. If the large package has 10 pens, how mar pencils are in the large package?
Answer:
4 pencils.
Step-by-step explanation:
The ratio of pencils to pens in the original package is 10:4, which means that for every 4 pens, there are 10 pencils. To find the number of pencils in the larger package, we can use this same ratio.
If the large package has 10 pens, we can set up the proportion:
x/10 = 10/4
Where x is the number of pencils in the large package. To solve for x, we can cross-multiply:
10 * 4 = x * 10
40 = x*10
x = 40/10
x = 4
So the large package contains 4 pencils.
Chris is employed as a waiter in an upscale
restaurant. His restaurant pays him $5.75 per hour
during which time he can serve two groups. The
average tip per group is $8.75. Write an equation that
outputs Chris' total income (1) based on the number of
hours he works (h).
Equation that represents Chris's total income = ($5.75+$17.5) X, where X is the number of hours he works in a day.
What is equation?Equation is a mathematical statement that expresses the equality between two or more expressions.
Equation are different types such as equation with one variables and equation with two variables. The equation is used to determine the unknown values.
What is the equation that outputs Chris total income?Assume, Chris works X hours in a day.
He earns $5.75 per hour.
during his work time he serves two groups.
The average tip per group = $8.75
tips earned from two groups = $8.75 × 2 = $17.5
Outputs of Chris total income if he works total X hours in a day
= ($5.75+$17.5) X
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In a right triangle, given legs of lengths 5 and 12, find the length of the hypotenuse.
Answer:
13
Step-by-step explanation:
the using the Pythagorean Theorem A^2+b^2=c^2
5^2 is 25
12^2 is 144
add 144+25=169 then you square root this and it should be 13
or
A French restaurant used 203,640 ounces of cream last year. This year, due to a menu update, it used 65% less. How much cream did the restaurant use this year?
This year 71, 274 ounce cream used.
What is Percentage?To determine the quantity or percentage of something in terms of 100, use the percentage formula. Per cent simply means one in a hundred. Using the percentage formula, a number between 0 and 1 can be expressed. A number that is expressed as a fraction of 100 is what it is. It is mostly used to compare and determine ratios and is represented by the symbol %.
Given:
A French restaurant used 203,640 ounces of cream last year.
This, year 65% less cream used.
So, this year the amount of cream used
= 203640 - 203640 x 65%
= 203640 - 203640 x 0.65
= 203640 - 132366
= 71274 ounce
Hence, 71274 ounce cream used this year.
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A professional basketball player is 76 inches tall. A model of this player is 6
inches tall. Determine the simplified scale factor of the model to the real-life
player. Use colon notation. Then explain what the scale factor means.
The scale factor of the model to the real-life player is 6:76. This can be read as 6/76 or 0.0789 or 0.079(approximately)
The scale factor is a ratio that compares the size of the model to the size of the real-life object. In this case, the scale factor of 6:76 tells us that for every 76 inches of the real-life player, the model is only 6 inches. In other words, the model is 6/76 or approximately 0.0789 times smaller than the real-life player.
In general, a scale factor is a number used to multiply all the dimensions of an object to get a corresponding model or representation of that object, where the ratio of the corresponding dimensions between the real-life object and the model is represented by the scale factor.
It should be noted that the scale factor can also be represented in fraction or decimal form, but the colon notation gives a more meaningful representation of the comparison of the size between the model and the real-life object.
Answer: The scale factor for the basketball player to the model is 16 inches to 1 inch
Step-by-step explanation:
400 divide by 15=_ divide by 1/2
Answer:
53.333
Step-by-step explanation:
400/15 x 2 = 53.333
6. Find m4V.
Y
V
(10x-27)
(2x +29)
X
W
nswers 1-7
Since the total of the inner angles of the rhombus is 360 degrees, the angle mV has a value of 90.
what is angles ?In Euclidean geometry, an angle is a shape made up of two rays, referred to as the angle's sides, that come together at a point in the middle known as the angle's vertex. An angle that is in the plane where the rays are placed can be created by two rays. An angle is also produced when two planes collide. They are known as dihedral angles. In planar geometry, an angle is the form produced by two rays or lines that share a termination. The English word "angle" comes from the Latin word "angulus," which means "horn." The vertex, also known as the sides of the angle, is where the two rays' common terminals meet.
given
m∠V + m∠W + m∠X + m∠Y = 360
10x -27 + 2x + 19 = 180
12x - 8 = 180
188 = 12x
x = 15.66
m∠V + m∠X = 180
2x = 180
x = 90
Since the total of the inner angles of the rhombus is 360 degrees, the angle mV has a value of 90.
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Which shows the pre-image of triangle XYZ' before the figure was rotated 90° about the origin?
Answer: 2nd picture
Step-by-step explanation: its rotating 90 degrees
Multi-Step Linear Equations LC)
Solve −7x− 7 = −3x + 9 for x.
A: x = −4
B: x = −3
C: x = 3
D: x = 4
Answer:
A) x= -4
Step-by-step explanation:
-7x+3x=7+9
-4x= 16
x= 16÷ -4 = -4
Which graph represents the solution to the following sentence?
{x\x>4} U {x|x < -2}
-3 -2 -1 0 1 2345
-4 -3 -2 -1 0 1 2 3 4
-3 -2 -1 0 1 2 3 4 5
Answer: The graph represents the solution to the following sentence is the option number 3:
-3 -2 -1 0 1 2 3 4 5
This is because the set notation {x|x>4} U {x|x<-2} represents the union of all values of x that are greater than 4 and all values of x that are less than -2. The graph shows all the values of x that are greater than 4 and all values of x that are less than -2. The graph also includes the values of x between -3 and 5, it encompasses all the values that are greater than 4 and all values that are less than -2.
The graph represents the solution to the following sentence is (C).
What is Inequality?Mathematical expressions with inequalities are those in which the two sides are not equal. Unlike to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.
We have,
{x | x >4 } ∪ {x | x < -2}
Here the set notation {x|x>4} U {x|x<-2} represents the union of all values of x that are greater than 4 and all values of x that are less than -2.
The graph displays all instances of x larger than 4 and all instances of x less than -2.
The graph covers all x values higher than or equal to 4, as well as all x values less than or equal to -2.
It also includes x values between -3 and 5.
Thus, the number line is C.
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Can someone please actually solve this will mark brainlest and give five stars
In the circle the area of the shaded region and the length of arc ADB is 23/4 π and 23/6 π respectively.
What is length of arc?
The distance along the curved line that makes up the arc is measured using the arc length formula (a segment of a circle). The arc length is, to put it simply, the distance that passes through the curved line of the circle that forms the arc. It should be noted that the arc's length is greater than the separation of its ends along a straight line.
Given that the circle has a center O.
The radius of the circle is 3 yd.
The measure of ∠AOB is 130°.
First find the measure of ∠ADB -
∠ADB = 360° - ∠AOB
Substituting the values in the equation -
∠ADB = 360° - 130°
∠ADB = 230°
Now find the area of the shaded region.
The area of the shaded region can be determined using the formula -
A = (θ/360)πr²
Substituting the values in the equation -
A = (230/360) π(3)²
A = (230/360) π 9
A = 23/4 π or 5.75 π
Therefore, the area of the shaded region is 5.75 π yd².
Now, find the length of the arc ADB.
The length of arc ADB can be determined using the formula -
Arc Length = (θ/360)2πr
Arc Length = (230/360)2π3
Arc Length = 23/6 π or 3.83 π
Therefore, the length of arc is 3.83 π yd.
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Question
A proposed change in income tax suggests charging 20% on a person's income up to $30, 000 and then 40% on any
income above that. If a person has an income of $47, 000, what will be their income tax under the proposal?
Give your answer in dollars to the nearest dollar. Do not include commas or the dollar symbol in your answer.
The total income tax imposed on $47,000 is $12,800
How does income tax work?The term "income tax" describes a class of taxes that governments impose on income generated by people and businesses within their territorial jurisdiction.
Taxpayers are required by law to submit an income tax return each year in order to determine their tax obligations.
Income taxes are the main source of funding for governments. They are employed to fund public services, provide residents with goods, and settle debts owing to the government.
A number of states and municipal governments, in addition to the federal government, also require payment of income tax. The Internal Revenue Service is responsible for collecting taxes and enforcing the tax laws in the United States (IRS).
Regarding credits, deductions, and other forms of taxable and reportable income.
Firstly let us break the income tax as per the given condition
Income = 47,000 = 30,000 + 17,000
hence 20% tax is imposed on $30,000 and 40% on $17,000
Total income tax = 20% of 30000 + 40% of 17000
Total income tax = 6000 + 6800 = 12800
hence, The total income tax imposed on $47,000 is $12,800.
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(1,-9) and (-3,-9) in slope intrcept form
(Multiplying Linear Expressions MC)
Multiply 5c(9 − 4c).
A: 45c − 4c
B: 45c − 20c2
C: 45c − 20c
D: 45 − 20c2
Answer:
45c-20c²
Step-by-step explanation:
You just multiply the number outside the bracets with the numbers inside.
5c×9= 45c
5c×-4c= -20c²
So the answer is 45c-20c²
Which is option 'B'
13. Translate to an algebraic expression.
The result of subtracting j from 13
The algebraic expression for "the result of subtracting j from 13" can be written as 13 - j.
How do you construct an algebraic expression for subtraction?The signs of all the terms in the algebraic expression that is to be subtracted from another must be changed from "+" to "-" or from "-" to "+" before the two expressions are added.In algebra, subtraction is an operation that can be used to determine the difference between two numbers. Subtraction is represented by the minus sign (-).When subtracting, the number being subtracted from is called the minuend, and the number being subtracted is called the subtrahend. To subtract j from 13, the minuend is 13, and the subtrahend is j.Therefore, the algebraic expression for "the result of subtracting j from 13" can be written as 13 - j.Subtraction is a fundamental operation in algebra which can be used to solve many types of problems.It can be used to determine the difference between two numbers, as well as to solve equations.For example, if the equation 5x - j = 13 is given, we can use subtraction to solve for x.To do this, we would subtract j from both sides of the equation, resulting in the equation 5x = 13 - j.We can then divide both sides by 5 to get x = (13 - j) / 5. Therefore, the result of subtracting j from 13 is (13 - j).
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Customers who purchased two different computer models were asked if they were happy with their purchase. The results are shown in this table. Drag and drop the correct percentage to complete each statement. Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse. Of those who were not happy with their purchase, about Response area purchased model A, and about Response area purchased model B. 6%18%20%26%36%82% Happy Not happy Purchased Model A 8 2 Purchased Model B 16 9
Of those who were not happy with their purchase, about 20% purchased model A, and about 36% purchased model B.
Illustrate the satisfaction level among customers?Of those surveyed who purchased two different computer models, about 82% reported being happy with their purchase. Of those who were not happy, about 6% purchased model A and 18% purchased model B. This suggests that customers were more satisfied with model A than model B.Additionally, 20% of those who purchased model A were not happy, while 26% of those who purchased model B were not happy. This demonstrates that more customers were unhappy with model B than model A. Overall, it appears that customers were generally satisfied with their purchases, though there is room for improvement in terms of customer satisfaction with model B.This table shows the responses from customers who purchased two different computer models. Of those who were happy with their purchase, 82% purchased Model A and 18% purchased Model B. Of those who were not happy with their purchase, 6% purchased Model A and 26% purchased Model B.This table helps to illustrate the satisfaction level among customers who purchased the two different computer models. This kind of data is useful for companies to identify which models are the most successful, and which ones may require additional improvements.To learn more about to illustrate the satisfaction level among customers refer to:
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Suppose the set A = U. How many elements are [tex]A^{c}[/tex]
The number of elements in [tex]A^c[/tex] is zero.
What is a set?A set is a collection of items where there are operations such as:
Union of sets, the intersection of sets, and the complement of sets.
We have,
U = universal set
This includes all values.
[tex]A^c[/tex] = complement of set A.
This means,
All the elements of U except the elements of A.
[tex]A^c[/tex] = U - A
Now,
If A = U,
[tex]A^c[/tex] = U - U = 0
Thus,
There are no elements in [tex]A^c[/tex].
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Write an equation that represents the line.
Use exact numbers.
Please help quickly!! my test is due soon!!
On solving the provided question, we can say that from the given graph, it is shown that it is a starlight line so the equation that represents is x = y => x-y = 0
What is graphs?Mathematicians use graphs to logically convey facts or values using the visual representations or charts. A graph point will typically reflect a relationship between two or more things. Nodes, or vertices, and edges make form a graph, a non-linear data structure. Glue together the nodes, often referred to as vertices. This graph has vertices V=1, 2, 3, 5, and edges E=1, 2, 1, 3, 2, 4, and (2.5), (3.5). (4.5). Statistical charts (bar charts, pie charts, line charts, etc.) graphical representations of exponential growth. a logarithmic graph in the shape of a triangle
here, from the given graph
it is shown that it is a starlight line
so the equation that represents is x = y
x-y = 0
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4x = 8x − 1 (5 points) x = three fourths x = 1 x = 3 x = 6
For expression 4x=8x-1, x will be 1/4.
what are expressions?
Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between. The mathematical operators can be of addition, subtraction, multiplication, or division. For example, x + y is an expression, where x and y are terms having an addition operator in between. In math, there are two types of expressions, numerical expressions - that contain only numbers; and algebraic expressions- that contain both numbers and variables.
e.g. A number is 6 more than half the other number, and the other number is x. This statement is written as x/2 + 6 in a mathematical expression. Mathematical expressions are used to solve complicated puzzles.
Now,
As given expression is 4x=8x-1
8x-4x=1
4x=1
x=1/4
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Use the table to write a linear function that relates y to x
Answer:
From the table, we can see that the y value is always -7, regardless of the x value. This means that the y-intercept of the function is -7.
Step-by-step explanation:
From the table, we can see that the y value is always -7, regardless of the x value. This means that the y-intercept of the function is -7.
Therefore, the linear function that relates y to x, using this table, is:
y = -7
It's a constant function, no matter what the x value is, the y value is always -7.
This system of linear inequalities can be used to find the possible heights, in inches, of Darius, d, and his brother William, w.
d ≥ 36
w < 68
d ≤ 4 + 2w
Which statements must be true about their heights? Select three options.
Darius is at least 36 inches tall.
Darius is at most 36 inches tall.
William’s height is less than 68 inches.
William’s height is at least 68 inches.
Darius is less than 4 inches taller than twice William’s height.
Darius is no more than 4 inches taller than twice William’s height.
Since this system of linear inequalities can be used to find the possible heights, in inches, of Darius, d, and his brother William, w, the three statements which must be true about their heights include all of the following:
A. Darius is at least 36 inches tall.
C. William’s height is less than 68 inches.
F. Darius is no more than 4 inches taller than twice William’s height.
How to write and interpret the system of inequalities graphically?In order to write a system of linear inequalities to describe this situation, we would assign variables to the possible heights, in inches, for Darius and Williams, and then translate the word problem into algebraic equation as follows:
Let the variable d represent the Darius's height.Let the variable w represent the number of William’s height.Next, we would interpret the given system of linear inequalities as follows;
d ≥ 36 ⇒ "Darius is at least 36 inches tall." because of the greater than or equal to (≥) inequality symbol.
w < 68 ⇒ "William’s height is less than 68 inches." because of the less than (<) to inequality symbol.
Additionally, d ≤ 4 + 2w ⇒ "Darius is no more than 4 inches taller than twice William’s height." because of the less than or equal to (≤) inequality symbol.
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what percent of 40 is 50?
Answer:20
Step-by-step explanation:
Answer:
the percent of 40 is 50
the answer to this is 10
What is the quotient of -231 and 3
Answer :-77. ✅
Step-by-step explanation:
To find the quotient of -231 and 3, we divide -231 by 3.
-231 ÷ 3 = -77
The quotient of -231 and 3 is ✅
Solve for x. -3x - 6 = -4x + 5
The solution to the equation -3x - 6 = -4x + 5 is x = 11.
What is equation?
An equation is a mathematical statement that uses an equals sign (=) to show that two expressions have the same value.
To solve for x in the equation -3x - 6 = -4x + 5, we need to isolate the variable x on one side of the equation. We can do this by adding 4x to both sides of the equation to eliminate the negative 4x term on the right-hand side:
-3x - 6 + 4x = -4x + 5 + 4x
Simplifying the left-hand side by combining like terms, we get:
x - 6 = 5
Finally, to isolate x, we add 6 to both sides of the equation:
x - 6 + 6 = 5 + 6
Simplifying the left-hand side and the right-hand side, we get:
x = 11
Therefore, the solution to the equation -3x - 6 = -4x + 5 is x = 11.
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Alex is purchasing 3 concert tickets. The website charges a $5 fee for each ticket. Her total is $117. What is the original cost of each concert ticket? Choose the equation that represents the situation.
The original cost for each concert ticket is given as follows:
$34.
How to obtain the original cost for each concert ticket?The original cost for each concert ticket is obtained applying the proportions in the context of this problem.
The fee for a single ticket is divided as follows:
$5 fee for the website.$n fee for the original cost.Hence the proportional relationship that models the cost of purchasing x tickets is given as follows:
y = (5 + n)x.
Alex purchased 3 concert tickets, meaning that x = 3, for a total of $117, meaning that y = 117, hence the original cost n is obtained as follows:
117 = (5 + n) x 3
Dividing by 3 on both sides, we have that:
5 + n = 39
n = 39 - 5
n = $34.
Which is the original cost for each concert ticket.
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Answer one of the following questions
HELPPPP ASAPPPP!!!!
Solve:
2x-10
———- = 3x
4
X = -10
X = -1
x = 2
X = 11
The solution of this equation is given by x = -10 ( option A)
What is an equation ?The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
A mathematical statement that has a "equal to" symbol between two expressions with equal values is called an equation. as in 3x + 5 Equals 15, for instance. Equations come in a variety of forms, including linear, quadratic, cubic, and others. In this tutorial, let's study more about math equations.
The equation is
2x - 10 = 3x
⇒ x = -10
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