The value of the variable x when the distance between two points is 10 is equal to 13 or 1.
As given in the question,
Given two points (7, 5) and (x, -3)
Distance between two points (7, 5) and (x, -3) is equal to 10 units
Distance = √ ( y₂ - y₁ )² + ( x₂ - x₁ )²
⇒ (10) = √ ( -3 -5 )² + ( x - 7 )²
⇒ 10 = √ ( -8 )² + x² - 14x + 49
⇒ 10² = 64 + x² - 14x + 49
⇒ 100 = 113 + x² - 14x
⇒ x² -14x + 13 = 0
⇒ x² -13x -x + 13 =0
⇒ ( x - 13) ( x - 1) = 0
⇒ x = 13 or 1
Therefore, the value of the variable x for the given distance and points is equal to 13 or 1.
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Is it possible to create a system of inequalities that has no solution? If so, create one and explain how the graph would show no solutions. If not, explain why.
Answer: See explanation.
Step-by-step explanation:
Any false inequality has no solution. For example |x+3|<-2 has no solutions for x. The graph would not display any answers for x as there is no solution due to the absolute value.
The relationship between x and y can be modeled by an inverse variation function what is the value of k for the inverse variation function? k =.
In the inverse variation function, when x and y are given, the value of k will be K = x * y.
Inverse variation states that when the value of one quantity increases, then the value of another quantity decreases in the same proportion. It includes a relationship between variables that are mentioned as y=k/x where x and y are variables and k is constant.
Distance and speed can be taken as a great example of inverse variation. When speed increases distance decreases.
When 'K' is constant, we can find it by multiplying the x-coordinate by the y-coordinate. So, we can say that in an inverse variation function, when x and y are given, the value of 'k' will be K =x*y.
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In a city in Ohio, the sales tax rate is 7.25%. Complete the table.
there were 425 guests at a hotel. 170 guests ordered food. what percentage of the guests ordered food?
Answer:
255
Step-by-step explanation:
If 422 guests were at a hotel and 170 ordered food, The percentage of food would clearly be 255.
What type of word is splitting?
Answer:
Splitting is where numbers in an equation are broken apart to make it easier to calculate.
Step-by-step explanation:
Splitting is where numbers in an equation are broken apart to make it easier to calculate. Ex:
21 * 7
20 * 7 + 1 * 7 =
140 + 7
147
A costume rental store charges a fixed refundable security deposit plus an amount per
day that the costume is rented. The table shows the total cost to rent a costume for x
days. What is the initial value?
Number of Days (x) Total Cost (y)
# of days (x)
1
2
3
4
Total Cost(y)
41
48
55
62
The initial value is___
Answer:
The initial value in the given table is 41. This is the total cost to rent a costume for 1 day, which is the smallest number of days listed in the table. The initial value represents the fixed refundable security deposit that the costume rental store charges, which is a constant amount that does not depend on the number of days the costume is rented for.
Step-by-step explanation:
which assumption of ols assumes that there is no correlation between the error and the independent variables
The regression model is assumption of ols assumes that there is no correlation between the error and the independent variables
What is the Assumption of Linearity?
Linearity Assumption (OLS Assumption 1) - The model will be inaccurate and therefore unreliable if it is fitted to data that is not linearly connected. Extrapolating from the model is likely to produce inaccurate results. As a result, you must always draw a graph of the observed and anticipated values. The linearity assumption is confirmed if the graph is symmetrically distributed over the 45-degree line. By applying non-linear transformations to the independent variables, you can change the functional form of the regression if the linearity requirements are violated.
The OLS assumption of no multi-collinearity says that there should be no linear relationship between the independent variables.
Hence, The regression model is the assumption of ols assumes that there is no correlation between the error and the independent variables.
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Janet, an antique dealer, purchaed a claic toy car a an
invetment. She wrote the equation y = 40x 100 to repreent
the value y in dollar of her invetment x year after he bought it. What are the initial value and rate of change! Explain
Using the provided equation and derivative for the rate, The initial value is 100 and the rate is 40.
What do you mean by equations?The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions.
What do you mean by derivative?in mathematics, the rate of change of a function with respect to a variable. Derivatives are fundamental to the solution of problems in calculus and differential equations.
y= 40x + 100
x=0 for initial value, We get y=100.
apply derivative on y with respect to x , We get
[tex]\frac {dy}{dx} =40[/tex]
rate =40
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the system of equations models the price per share, y, for two stocks overtime, x. which represents the viable solution to the system? -y<= 3x+4-3x-3y<=-9. A. all real number values of x and y.
B. all real number values, with x >=0
C. all real number values, with y >=0
D. all real number values, with x >=0 and y>=0
The option that describes the viable solution for the system is D.
all real number values, with x >=0 and y>=0
Which can be a viable solution for the system?Here we have the following system of inequalities:
-y ≤ 3x + 4
-3x - 3y ≤ 9
We can rewrite the second inequality to get:
-3y ≤ 9 + 3x
-y ≤ 9/3 + 3x/3
-y ≤ 3 + x
Then our system of inequalities becomes:
-y ≤ 3 + x
-y ≤ 3x + 4
So, as long as x and y are both positive or 0, the system is true (this is a rough estimation), but that is enough to conclude that the correct option is D.
all real number values, with x >=0 and y>=0
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PLEASE HELP I will give brainiest!
Answer:
[tex]\frac{5}{3}[/tex]
Step-by-step explanation:
Because the problem is written as:
[tex]x^{3}[/tex] =
You look for the option that would equal [tex]\frac{125}{27}[/tex] when multiplied by itself 3 times,
[tex]\frac{5}{3}[/tex] x [tex]\frac{5}{3}[/tex] x [tex]\frac{5}{3}[/tex] = [tex]\frac{125}{27}[/tex]
C. [tex]\frac{5}{3}[/tex] is your answer ( because [tex]\frac{5}{3}[/tex] x [tex]\frac{5}{3}[/tex] x [tex]\frac{5}{3}[/tex] = [tex]\frac{125}{27}[/tex] )
[tex]x^{3}[/tex] = [tex]\frac{5}{3}[/tex] x [tex]\frac{5}{3}[/tex] x [tex]\frac{5}{3}[/tex] = [tex]\frac{125}{27}[/tex]
Hope this is helpful!
A poker hand coniting of 4 card i dealt from a tandard deck of 52 card. Find the probability that the hand contain exactly 2 face card
According to the given statement the probability that the hand contain exactly 2 face card is [tex]\frac{1}{221}[/tex].
Simple probability: What is it?Calculating a result or perhaps the probability that an event would ever occur is known as simple probability. Probability statistics are used by insurance firms to calculate the probability that they'll have to give out a claimed. By dividing one possible outcome by all other possible possibilities, one may determine a basic probability.
Briefing:A regular 52-card deck is used to deal a poker hand, which consists of 4 cards.
The total number of cards in a deck 52
Number of faces cards in a deck = 2
Number of cards not face cards = 50
The total number of combinations of drawing 4 cards out of 52 cards = [tex]={ }^{52} C_4[/tex]
Now , the combination of 4 cards such that exactly 2 of them are face cards = [tex]{ }^{2} C_2 \times{ }^{50} C_2[/tex]
That probability that perhaps the collection will comprise exactly six face cards is as follows:
= [tex]\frac{{ }^{2} C_2 \times{ }^{50} C_2}{{ }^{52} C_4}[/tex]
[tex]=\frac{\frac{2 !}{2 ! 0 !} \times \frac{50 !}{2 ! 48 !}}{\frac{52 !}{4 ! \times 48 !}}[/tex]
=[tex]\frac{1}{221}[/tex]
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What are the 3 formulas for slope?
The three formulas for slope are: Slope formula, slope-intercept formula, and at the point-slope formula
1. Slope formula : (y2-y1) / (x2-x1)
2. Slope intercept formula: y = mx + b
3. Point slope formula: y - y1 = m(x - x1)
The slope is defined as the steepness of a line, which is described by the ratio of the vertical change between two points (rise) over the horizontal change between the same two points (run). The first formula is the most commonly used and is used when we know two points in a line. The second formula is a for the slope and y-intercept and the third one is the slope of a line and a point on the line.
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Which is an equation of the line that passes through (–4, –5) and (–5,–7)
The equation of line that passes through points (-4, -5) and (-5, -7) is 2x - y + 3 = 0.
What is equation of line?A line's equation is an algebraic way of expressing the collection of points that make up a line in a coordinate system.
The many points that collectively make up a line on the coordinate axis are represented as a group of variables (x, y) to create an algebraic equation, also known as an equation of a line.
The formula for equation of line that passes through points (x₁, y₁) and having slope m is, y - y₁ = m (x - x₁)
The given points are (-4, -5) and (-5, -7)
To find the equation of line, use formula,
y - y₁ = m (x - x₁)
Where m = (y₂ - y₁) / (x₂ - x₁)
For the points (-4, -5) and (-5, -7),
The slope m = (-7 - (-5)) / (-5 - (-4)) = (-7 + 5) / (-5 + 4) = -2 / -1 = 2
The required equation of line,
y - (-5) = 2 (x - (-4))
y + 5 = 2 (x + 4)
y + 5 = 2x + 8
2x - y + 3 = 0
The required equation of line is 2x - y + 3 = 0.
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Conor is going to the movie theater. A ticket to a movie costs t dollars, and there is a 15% amusement tax on each ticket.
a. Conor buys a ticket to see a movie. Write two expressions in terms of t showing his total cost.
b. The price of a movie ticket is $12.49. Use one of the expressions you wrote in part a to find Conor’s total cost, rounded to the nearest penny. Show your work.
a) Two mathematical expressions in terms of t showing Conor's total cost for going to the movie theater are:
1) 1.15t2) t + 0.15t.b) Using one of the mathematical expressions above, Conor's total cost for going to the movie theater is $14.36.
What are mathematical expressions?Mathematical expressions are combinations of numbers and variables, using mathematical operations such as addition, subtraction, multiplication, division, and exponentiation.
Mathematical expressions are also known as algebraic expressions.
The cost of a ticket to a movie = t dollars
Amusement tax on each ticket = 15%
a) Mathematical Expressions to model the total cost, t:
Total cost = 1.15t
Total cost = t + 0.15t
b) Price of a movie ticket = $12.49
Conor's total cost = 1.15(12.49)
= $14.36
Using algebraic expressions, when Conor purchases a movie ticket for $12.49, including a 15% amusement tax, brings the total cost to $14.36.
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Does A and B have the same solution
A. 4x + 2 = 6 - x
B. 5x + 2 = 6
Answer:
No, A and B do not have the same solution.
To find the solution to A, we need to isolate the variable x on one side of the equation and solve for its value. We can do this by subtracting x from both sides of the equation and then adding 2 to both sides. This gives us:
4x + 2 - x = 6 - x + 2
3x = 8
x = 8/3
To find the solution to B, we need to isolate the variable x on one side of the equation and solve for its value. We can do this by subtracting 2 from both sides of the equation. This gives us:
5x + 2 - 2 = 6 - 2
5x = 4
x = 4/5
As we can see, the solutions to A and B are different, so A and B do not have the same solution. The solution to A is x = 8/3, and the solution to B is x = 4/5.
Step-by-step explanation:
at a large university, data were collected on the number of sisters and brothers that each student had. let the random variable x represent the number of sisters and the random variable y represent the number of brothers. the distribution of x has mean 1.00 and standard deviation 0.94. the distribution of y has mean 1.07 and standard deviation 1.04. what is the mean of the distribution of x y ?
The required mean of the distribution of x + y for the given data is 2.07.
Explain mean distribution.A statistical distribution, or probability distribution, portrays how values are dispersed for a field. As such, the measurable dissemination shows which values are normal and exceptional. There are numerous sorts of measurable appropriations, including the chime formed typical conveyance.
According to question:We have,
mean = 1 and Standard deviation = 0.94
In distribution of Y
mean = 1.07 and standard deviation = 1.04
mean of distribution X + Y = ?
Then,
the mean of the distribution of X+Y
= mean of x + mean of y
= 1 + 1.07
= 2.07
Thus, the required mean is 2.07.
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What is the formula of time?
The formula of time is time: distance/speed
Time is an important concept in physics, and it can be expressed in a variety of ways. The most common way to describe time is with the equation t = d/s, where t is time, d is the change in position of an object, and s is the speed of the object. This equation is known as the time-distance formula. The time-distance formula can be used to calculate the time it takes for an object to travel a certain distance., also the time-distance formula can also be used to calculate the distance an object travels in a certain amount of time.
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Explain whether this dilation is an enlargement or a reduction, and how you know. Triangle a b c is enlarged to triangle a prime b prime c prime.
Triangle ABC to triangle A'B'C' is enlarged by the dilation.
What is meant by dilation?Dilation is the process of enlarging a shape, figure, or line. In mathematics, dilation means Reducing the object's size by dilation is a change. The items are enlarged or shrunk through dilation. An image that retains the original shape is created by this alteration. A dilation in mathematics is a function f from a metric space M into itself that fulfills the formula d=rd for all locations x, y in M, where d is the distance between x and y and r is some positive real number. A resemblance of the space exists in Euclidean space when a dilation like this occurs.
The query leads us to believe that:
Triangle A'B'C' is created by enlarging triangle ABC.
The diagram also demonstrates that triangle A'B'C"s side lengths are longer than ABC's.
The dilation is hence an augmentation
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Answer:
The dilation is an enlargement because the image, triangle A'B'C', is larger than the pre-image, triangle ABC.
Step-by-step explanation:
edge 2023
There are 7 songs on each CD. If
you have 60 CD's, how many total
songs will you have?
Answer:
420
Step-by-step explanation:
60 x 7 = 420
Answer: 420
Step-by-step explanation:
If you have 7 songs on each CD then you have 60 CD'S just take 7 and times it by 60.
If three apples cost $1.97, how much would six apples cost?
Answer:
$3.94
Step-by-step explanation:
Since it is three apples and we want to know how much six apples would cost, we should just multiply $1.97 by 2. We have to double it.
1.97x2= $3.94
Answer:
$3.94
Step-by-step explanation:
So if 3 apples cost $1.97, then 6 apples cost twice that.
$1.97 x 2 = $3.94
what is the value of the expression when m = 2.5 and n = 5
Answer: 13.1
Step-by-step explanation:
(2.5)+(7*9)/(5) = 2.5+63/5 = 65.5/5 = 13.1
Answer:
13.1
Step-by-step explanation:
Given rational expression:
[tex]\dfrac{m+(7 \cdot 9)}{n}[/tex]
To determine the value of the given expression when m = 2.5 and n = 5, substitute the given values into the expression and solve.
[tex]\begin{aligned}m=2.5, n=5 &\implies \dfrac{2.5+(7 \cdot 9)}{5}\\\\&\implies \dfrac{2.5+63}{5}\\\\&\implies \dfrac{65.5}{5}\\\\&\implies \dfrac{65.5 \cdot 2}{5 \cdot 2}\\\\&\implies \dfrac{131}{10}\\\\&\implies 13.1\end{aligned}[/tex]
How do you find the maximum number?
To find the maximum number in a list of numbers, we go through the whole list of numbers and compare each values.
We know that the maximum number is nothing but a number having the largest value in the data set.
To find the maximum number in a list of numbers, we go through the whole list of numbers and compare each values.
The maximum number in the list is the largest value found when all values have been compared.
For example, in the list of numbers 23, 98, 76, 90, 17, 71
the maximum number is 98
Therefore, the maximum number in the list is the largest value found when all values have been compared.
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Steven has a credit card with a line of credit at $2,500. He made the following purchases: $405.36, $300.33, $317.11, and $94.20. What is his available credit?
Answer: It's either 60 or 232
Note: I'm not that good, in problem solving but i thought i can try.
Message: If this helps, let me know by giving me a thanks! :)
Alexander uses cupric chloride to etch circuit boards. He recorded the room temperature, in ^\circ\text{C}
∘
Cdegrees, start text, C, end text, and the etching rate, in \dfrac{\mu\text{m}}{\text{min}}
min
μm
start fraction, mu, start text, m, end text, divided by, start text, m, i, n, end text, end fraction, of the cupric chloride.
After plotting his results, Alexander noticed that the relationship between the two variables was fairly linear, so he used the data to calculate the following least squares regression equation for predicting the etching rate from the room temperature:
\hat y = 2 +\dfrac{1}{5} x
y
^
=2+
5
1
xy, with, hat, on top, equals, 2, plus, start fraction, 1, divided by, 5, end fraction, x
What is the residual if the room temperature was 25^\circ\text{C}25
∘
C25, degrees, start text, C, end text and the cupric chloride had an etching rate of 5\dfrac{\mu\text{m}}{\text{min}}5
min
μm
5, start fraction, mu, start text, m, end text, divided by, start text, m, i, n, end text, end fraction ?
\dfrac{\mu\text{m}}{\text{min}}
min
μm
The residual, if the cupric chloride had an etching rate of 5 [tex]\frac{\mu m}{min}[/tex], is given as follows:
-2 [tex]\frac{\mu m}{min}[/tex]
How to obtain the residual?For a data-set, the definition of a residual is that it represents the difference of the actual output value by the predicted output value, that is:
Residual = Observed - Predicted.
The predicted etching rate for a temperature of x in this problem is given by the line of best fit, defined as follows:
y = 2 + 1/5x.
Hence, for a temperature of 25ºC, the estimated etching rate is given as follows:
y = 2 + 1/5(25) = 2 + 5 = 7.
The observed etching rate is of 5 units, hence the residual is calculated as follows:
Residual = Observed - Predicted.
Residual = 5 - 7
Residual = -2.
Missing InformationThe problem is given by the image shown at the end of the answer.
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the coast (in dollars) of a custom-made t-shirt is represented 0.75n+9.99,where n is the number of words in the design.write and interpret a simplified expression that represents the coast the coast of 12 t-shirts
The 0.75 represents the cost of the custom of each t-shirt and 9.99 represents the cost of custom shipment. And the total cost of 12 t-shirts is $18.99.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
The cost (in dollars) of a uniquely crafted shirt is addressed as 0.75n + 9.99, where n is the number of words in the plan.
The cost of 12 t-shirts will be given as,
⇒ 0.75n + 9.99
⇒ 0.75 x 12 + 9.99
⇒ 9 + 9.99
⇒ 18.99
The 0.75 represents the cost of the custom of each t-shirt and 9.99 represents the cost of custom shipment. And the total cost of 12 t-shirts is $18.99.
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When a train of length of 150 m is Travelling at a speed of 54 km per hour How much time does it take to cross 1 electric pole?
The train will take 10 seconds to cross 1 electric pole at the speed of 54 kilometres per hour.
The time taken will be calculated by the formula- time = distance/speed.
Now firstly converting the speed to meter per second.
As we know, 1 km is 1000 meters and 1 hour has 3600 seconds. Thus, speed = (54 × 1000)/3600
Cancelling zero and performing multiplication and division
Speed = 15 m/s.
Keep the values in formula -
Time = 150/15
Performing division
Time = 10 seconds
Hence, it takes 10 seconds by the train.
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Find the slope and y-intercept of each line from the given equation.
y = 3x + 4
Slope:
y-intercept:
y = -2x - 3
Slope:
y-intercept:
I just need it answered clearly, I HAVE to pass this quiz.
y= 3x + 4
Slope: 3
y-intercept: (0,4)
y= -2x - 3
Slope: -2
y-intercept: (0,-3)
Carson and Romeo are floating in a lake. They each
start swimming away from the shore.
The graph shows that the two lines in the system of
equations that represent Carson's and
Romeo's distances from shore over time are the
same lines.
Distance from Shore
The completed statement that described the situation indicated by the graph of the linear system of equations representing Carson and Romeo distance from the shore is presented as follows;
The graph of the system of equations show that Romeo was floating close to Carson and then swam alongside Carson
The system of equations represented on the graph has an infinite number of solutions because the two lines in the system of equations are the same line
What is a linear system of equations?A system of linear equations are a set of linear equations that are formed by the same variables, and which work together.
The points on the graph of the equation, obtained from a diagram of a similar question online are; (0, 5), (1, 6), (2, 7), (3, 8), (4, 9) (5, 10)
Therefore, the slope of the equation representing the distance from the shore is, m = (6 - 5)/(1 - 0) = 1
The y-intercept, the point where x = 0, is (0, 5), which indicates that the y-intercept is c = 5
The equation of the line in slope-intercept form, y = m·x + c, therefore is; y = x + 5
Please find attached the graph in the question of the equation created with MS Excel
The details of the question obtained from a similar question on the internet indicate that the graph of the equation of Carson's distances and the graph of the equation of Romeo's distances are the same straight lines.
The y-intercept of the graph represent the location where the Carson and Romeo where initially floating, therefore;
Romeo was floating close to Carson
The coinciding graphs indicates that Carson and Romeo swam side by side
The equations of the distances which are equivalent, indicates that the system of equations has an infinite number of solutions
The reason the system of equations have an infinite number of solutions is because the two lined overlap
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5.11.7 Check Your Understanding
Valerie takes, on average, 30 mins, to drive the 11.8 miles to her job everyday.
How many total hours will Valerie have driven to work on average after 10 days?
How many hours, on average, will it take Valerie to drive a total of 224.2 miles to work?
How many days did Valerie drive to work if the total number of miles she drove was 247.8 miles
The results obtained by using proportions to calculate are:
A) Valerie takes (4.995 ≅) 5 hours to drive to work on average after 10 days.
B) Valerie takes (9.4911 ≅) 9.5 hours to drive a total of 224.2 miles to work.
C) Valerie takes (20.98 ≅) 21 days to drive a total of 247.8 miles to work.
How to write proportions?Proportions are the two ratios that are related by equality between them. I.e., w : x = y : z
We can rewrite them as
w/x = y/z or wz = xy
By using this relation, we can solve any of the variables.
Calculation:It is given that,
Valerie takes, on average, 30 mins, to drive the 11.8 miles to her job every day.
So, from this, we can find the time taken by her for driving 1-mile using proportions.
I.e.,
for 11.8 miles → 30 min
then 1 mile → X min
⇒ 11.8 : 1 = 30 : X
⇒ 11.8X = 30
∴ X = 30/11.8 = 2.54 mins
A) The time it takes for her to drive to work on average after 10 days:
for 10 days, she drives 11.8 × 10 = 118 miles
So, the time taken for 118 miles × 2.54 min = 299.72 min
We know that for 60 min it is 1 hour, then for 299.72 min, it is 4.995 hours that is on average Valerie takes 5 hours to drive for 10 days.
B) The time it takes for her to drive a total of 224.2 miles to work:
We know that for 1 mile she takes 2.54 min, then for 224.2 miles, she takes 224.2 × 2.54 = 569.468 min
That means 569.468 min/60 = 9.49 hours ≅ 9.5 hours
Thus, she takes 9.5 hours to drive 224.2 miles.
C) The number of days she takes to drive a total of 247.8 miles to work:
We know that for 1 mile she takes 2.54 min, then for 247.8 miles, she takes 247.8 × 2.54 = 629.412 min
If she takes 30 min to drive per day, then the number of days for 629.412 min is
= 629.412 min/30 = 20.98 days ≅ 21 days.
Thus, she takes 21 days for driving 247.8 miles.
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5. Sherman bought 17
items at the dollar store,
and used a coupon for a
discount. If his total after
the coupon was $16.15,
what percent discount did
he get?
Answer:
Step-by-step explanation: if you subtract 17 from 16.15 you will get your answer of 0.85 so if you turn that to a percentage you will get .00085