The equation of the line that is parallel to the line y = −2x +5 and passing through the point (1, −4) is y = -2x - 2.
How to form an equation?Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.
The slope of two parallel lines is always the same.
The slope y-intercept form of an equation is y = mx + c where m is the slope.
Given the parallel equation y = -2x + 5 by compare slope = -2
Therefore,the equation will become y = -2x + c
Substitute,(1,-4) into this
-4 = -2(1) + c ⇒ c = -2
So equation converts as y = -2x - 2.
Hence "The equation of the line that is parallel to the line y = −2x +5 and passing through the point (1, −4) is y = -2x - 2".
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Jane wants to save $500 to purchase a new television. She earns $10.50 an hour at her job. The function M(h) = 8h represents the amount of money Jane earns in dollars, M(h), for each hour h that she works. Find M(60).
*Type in your answer.
M(60) =$.
The amount that Jane would earn for working for 60 hours is $630.
What is M(60)?The given function is a linear function. A linear function is a function that changes at a constant rate. When a linear graph is drawn on a coordinate graph, it can slope either upward or downward.
The linear function that represents the total amount she earns is:
Total earnings = cost per hour x total number of hours worked
Total earnings = $10.50 x h
Total earnings = $10.50 x 60 = $630
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Write an equation of a line that goes through (4, 1) and has a slope of 2.
Please solve for y. There should be no actual numbers besides for 9.
Answer:
y= x/(n-9)
Step-by-step explanation:
Move 9 to the right side to get n-9
Take y over to get x=y(n-9)
Then shift n-9 over to other side to get y= x/(n-9)
1. What is the slope of a line Parallel to y=-2/3x - 7*3/2-3/2O 2/3-2/3
Question:
Solution:
The definition of parallel lines tells us that if two lines are parallel, they have the same slope. On the other hand, the slope-intercept form of a line is given by the following formula:
y = mx+b
where m is the slope of a line. In this case, the slope of the given line would be m = -2/3. Then the correct answer would be:
[tex]-\frac{2}{3}[/tex]What is Y=2x+5 solved
The answer of the linear equation for Y=2x+5 is x = (y-5)/2.
What is linear equation?
An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation. The standard form of a linear equation in one variable is of the form Ax + B = 0. Now in this equation, x is a variable, A is a coefficient, and B is constant.
The given linear equation is,
Y=2x+5
Now, solve this linear equation for x
Take 5 to LHS it will change sign to -ve
y-5 = 2x
Next, take coefficient of x below to LHS
(y-5)/2 = x
Now, swap the sides
x = (y-5)/2
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Please help!
Write an equation that represents the function graphed in blue by using transformations from y = |x| , which is graphed in green.
Answer:
-1/4*|X-1|Step-by-step explanation:
Let the green graph be G and the blue graph, be B:
1) Be cognate of the fact that the function in blue is completely negative, while the upper green graph is positive
Note: First, we should note that the blue function must therefore be a transformation of the Green function.
This means B takes the form:
y = (s)*a*|X+b|
We are required to find a, b, and s, where s is the sign.
2) From (1), we can deduce that, if graph G was transformed into B, then the first transformation begins by reflecting G along the X-axis (multiplying by -1).
Therefore, s = -1
3) From (2), it follows that the first transformation produces the following effect:
y = |X| transformed to y = -|X|
and B now takes the form y = -a*|X+b|
4) We notice again that the apexes of both functions do not touch. This means G was not only reflected along the X-axis but was also shifted or translated along the X-axis.
5) Building from (4), we notice that the Blue function takes a value of 0 when x is 1. If we put this in the general equation for B;
Finding b:
y = -a*|X+b| implies;
0= -a*|1+b|
|1+b| = 0/-a
|1+b| = 0
1+b = 0
b = -1and y becomes:
y = -a*|X-1|Finding a:
Notice also that when the x is 5, the Blue function now takes a value of -1. If we put this in a general equation for B;
y = -a*|X-1|
-1 = -a*|5-1|
-1 = -a*|4|
-4a = -1
a = 1/4The general equation for blue, B:y = -1/4*|X-1|Blaise M.
Select the value that make the inequality w≥6 true
Answer:
Every number that is greater than 6
the area of a right angled triangle is 96cm^2if the two shaded sides of the triangle differ by 2 what is the length of the shorter sides
The triangle have shorter sides of 12.9 and 14.9 cm, respectively
How to determine the lengths of the shorter sides?From the question, the given parameters are:
Triangle type = Right-angled triangleArea of triangle = 96 cm^2Also, from the question, we have:
Two shaded sides of the triangle differ by 2
In this case, the shaded sides of the triangle are
Opposite and Adjacent
This can also be interpreted as
Base and Height
So, we have
Base - Height = 2
The area is calculated as
Area = 0.5 * Base * Height
So, we have
0.5 * Base * Height = 96
This gives
0.5 * (Height + 2) * Height = 96
Divide by 0.5
(h + 2) * h = 192
Using a graphing calculator, we have
h = 12.9
Substitute h = 12.9 in Base - Height = 2
Base - 12.9 = 2
Evaluate
Base = 14.9
Recall that the Opposite and Adjacent are the shorter sides of a right triangle
Hence, the shorter sides are 12.9 and 14.9 cm
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Write an equation and solve.You bought a magazine for $5 and 4 erasers. You spent a total of $25. How much did each eraser cost?
Let the magazine be m and the eraser be e. Then the total cost is 25.
The equation can now be shown as follows;
[tex]\begin{gathered} 25=m+4e \\ 25=5+4e \\ Subtract\text{ 5 from both sides of the equation;} \\ 20=4e \\ \text{Divide both sides of the equation by 4} \\ 5=e \end{gathered}[/tex]Therefore each eraser cost $5
Spoonhead's
heart beats 48 times
per minute. How many times will
his heart beat in two hours?
Answer:5760
Step-by-step explanation:
48 beats per min and its 120 min in 2 hours so multiply 120×48=5760
Which of the following is not a condition necessary to create a valid probability distribution?
Given
different choices
Find
Which of the following is not a condition necessary to create a valid probability distribution?
Explanation
Each discrete outcome can have different probability of occuring
Hence the option stating each discrete outcome hsould have equal probability of occuring is not necessary
Final Answer
option (a) is correct option
1.39 to 1 decimal point
Answer: 1.4 or just 1
Step-by-step explanation:
But we are going to a decimal point then go to 1.4, cause the 9 makes the 3 round-up. :)
Answer: 1.4
Step-by-step explanation:
I believe you're asking what 1.39 rounded to the nearest tenths place is, in that case it is 1.4
Find 3 ratios that are equivalent to 6:15
Answer:12:30,2:5 and 18:45
Step-by-step explanation:
The volume of a gas V held at a constant temperature in a closed container varies inversely with its pressure P. If the volume of a gas is 800 cubic centimeters when the pressure is 450 millimeters of mercury (mm Hg), find the volume when the pressure is 200 mm Hg.
SOLUTION:
Step 1:
In this question, we are given the following:
The volume of a gas V held at a constant temperature in a closed container varies inversely with its pressure P. If the volume of a gas is 800 cubic centimeters when the pressure is 450 millimeters of mercury (mm Hg), find the volume when the pressure is 200 mm Hg.
Step 2:
This is an application of Boyle's law which states that:
Boyle’s law is a gas law that states that the pressure exerted by a gas (of a given mass, kept at a constant temperature) is inversely proportional to the volume occupied by it. In other words, the pressure and volume of a gas are inversely proportional to each other as long as the temperature and the quantity of gas are kept constant.
[tex]\begin{gathered} Mathematically,\text{ we have that:} \\ V\text{ }\propto\text{ }\frac{1}{P} \\ Then,\text{ we have that:} \\ V\text{ =}\frac{k}{P}\text{ \lparen where k is a constant \rparen} \end{gathered}[/tex][tex]when\text{ V = 800 cubic centimetres , then P = 450 mm Hg}[/tex][tex]\begin{gathered} 800\text{ =}\frac{k}{450} \\ cross-multiply,\text{ we have that:} \\ \text{k = 800 x 450 = 360,000} \end{gathered}[/tex][tex]\begin{gathered} Then,\text{ the equation connecting V and P =} \\ \text{ V }=\frac{360,000}{P} \end{gathered}[/tex]Next:
[tex]when\text{ P = 200 mm Hg, we have that:}[/tex][tex]\begin{gathered} V\text{ = }\frac{360,000}{200} \\ \text{V = 1800 cubic centimetres } \end{gathered}[/tex]CONCLUSION:
The volume when the pressure is 200 mm Hg is:
[tex]V\text{ = 1800 cubic centimetres}[/tex]Marty graphs the hyperbola (y+2)2/36−(x+5)2/64=1 .
How does he proceed?
Drag a value, phrase, equation, or coordinates in the boxes to correctly complete the statements.
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.
Marty first identifies the center of the hyperbola as Response area, and that the hyperbola opens Response area. Since a = Response area, the coordinates of the vertices are Response area.
The slopes of the asymptotes of this parabola are ± Response area, and the asymptotes pass through the center of the hyperbola. The equations of the asymptotes are Response area.
Once this information is gathered, the asymptotes are graphed as dashed lines, and the hyperbola is drawn through the vertices, approaching the asymptotes.
To construct the graph of the hyperbola, the procedure is as follows:
Marty first identifies the center of the hyperbola as (-5,2), and that the hyperbola opens up and down. Since a = 6, the coordinates of the vertices are (-5, -4) and (-5, 8).The slopes of the asymptotes of this parabola are a = ± 3/4, and the asymptotes pass through the center of the hyperbola. The equations of the asymptotes are y - 2 = ± 3/4(x + 5).Equation of an hyperbolaThe equation of a vertical hyperbola with center (x*, y*) is given according to the following equation:
(y - y*)²/a² - (x - x*)²/b² = 1.
A vertical hyperbola opens up and down.
In this problem, the equation is:
(y + 2)²/36 - (x + 5)²/64 = 1.
Hence the center is:
(-5, 2).
The value of coefficient a is:
a² = 36 -> a = 6.
Then the vertices of the hyperbola are:
(-5, 2 - 6) = (-5,-4).(-5, 2 + 6) = (-5,8).The slopes of the asymptotes of the parabola are given as follows:
±a/b.
Hence:
a/b = 6/8 = 3/4.-a/b = -6/8 = -3/4.Since the asymptotes pass through the center, the equation is:
y - 2 = ± 3/4(x + 5).
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we have a coin which, with equal odds, is either weighted so that heads has .75 probability, or weighted so that heads has .25 probability. we flip the coin twice and observe two heads. what is the conditional probability that the coin is weighted toward heads with .75 probability?
The Conditional Probability that the coin is weighted towards heads is 0.25/0.75 . Conditional probability is the result of Bayes’ Theorem .
A coin is tossed twice . So, total outcomes are { HH , TH , HT, TT} that is 4 .
Probability= favourable outcomes / total outcomes
Probability of getting two heads = ¼ = 0.25
Favourable outcomes are { HH , HT, TH}
Probability of getting at least one head = ¾ = 0.75
Conditional probability is measure of the probability of an event occurring, given that another event has already occurred.
Formula , P(A|B) = P(A and B)/ P(B)
Here, p(A|B) is conditional probability of A given B
P(B) is probability of event B occur
P(A and B) is probability of both events A and B occur
We have to find conditional probability that coin is weighted towards heads and it is = Probability of getting both heads / probability of getting at least one head
= ¼ / ¾ = 0.25 / 0.75
Which is required result .
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2.a statewide real estate sales agency, farm associates, specializes in selling farm property in the state of nebraska. its records indicate that the mean selling time of farm property is 90 days. because of recent drought conditions, the agency believes that the mean selling time is now greater than 90 days. a statewide survey of 100 farms sold recently revealed that the mean selling time was 94 days, with a standard deviation of 22 days. at the .10 significance level, has there been an increase in selling time?
The increase in the selling price is 1.818.
Test statistic:
A test statistic is a statistic used in statistical hypothesis testing. A hypothesis test is typically specified in terms of a test statistic, considered as a numerical summary of a data-set that reduces the data to one value that can be used to perform the hypothesis test.
The given values are:
a = 0.1
x = 94
μ = 90
The formula for test statistic will be:
t = ((x- μ) / ([tex]\frac{s}{vn}[/tex])
Now put the values in the given equation we have:
t = (94-90) / ([tex]\frac{22}{10}[/tex])
= 4/2.2
= 1.818
Therefore the increase in the selling price is 1.818.
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TEST SCORES The average test score in a class is 74%. Half of the class scored within 7 points of the average.
One student received a score of x%. Which shows an expression that could be used to determine how far the student's score is from the average?
A. |74-7|
B. |x|-74
C. |x-74|
D. 74-|7|
It is to be noted that the absolute expression that shows how far the student's score is from the average is given as: "| x - 74| (Option C)
What is the justification for the above result?The student obtained a score of x% based on the question. As a result, x% might be larger or lower than the average score of 74%.
To establish how distant the student's score is from the average, we must subtract the student's score from the average score; i.e. (x - 74)
This difference, however, might be negative: as a result, the absolute value of (x - 78) must be calculated, yielding |x - 74|.
As a result, the phrase that may be used to assess how distant the student's score is from the average is as follows: |x - 74| which is the same as option c - An Absolute expression.
Absolute expressions are or modulus of a real number x, abbreviated |x| in mathematics, is the non-negative value of x regardless of its sign.
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Answer this question for me
Answer:
3.97%
Step-by-step explanation:
You want to know the annual interest rate, compounded daily, that will result in $43,000 growing to $75,000 in 14 years.
FormulaThe formula for the account value is ...
A = P(1 +r/n)^(nt)
where P is the principal invested at annual rate r compounded n times per year for t years.
ApplicationFilling in the given values, we can solve for r.
75000 = 43000(1 +r/365)^(365·14)
75/43 = (1 +r/365)^5110 . . . . . divide by 43000 and reduce the fraction
Taking the 1/5110 power gives ...
(75/43)^(1/5110) = 1 +r/365 ≈ 1.00010886855
r/365 = 0.0010886855 . . . . subtract 1
r = 0.001086855·365 . . . . . multiply by 365
r ≈ 0.039737 = 3.9737%
The required interest rate is about 3.97%.
The graph shows g(x), which is a transformation of f(x)= 1x1. Write the function rule for
g(x).
The most appropriate choice for function will be given by -
g(x) = -|x| is the correct function
What is a function?
A function from A to B is a rule that assigns to each element of A a unique element of B. A is called the domain of the function and B is called the codomain of the function.
There are different operations on functions like addition, subtraction, multiplication, division and composition of functions.
f(x) = |x| is the given function.
f(x) has been transformed to g(x) according to the graph given in the figure
In the figure, the range is negative real number.
So the transformation g(x) = - |x|
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SAMANTHA HAS $27 TO RENT A BIKE FROM CYCLES RUS. SHE
HAS TO PAY A $IO FEE PLUS $2 FOR EVERY HOUR SHE HAS THE
BIKE. WRITE AND SOLVE AN INEQUALITY TO FIND THE
MAXIMUM NUMBER OF HOURS SAMANTHA CAN RENT THE BIKE.
Answer:
2 hours
Step-by-step explanation:
10+10= 20, so $20 fee
2+2= 4, so a fee for every hour she has the bike.
20+4= $24, so 2 hours maximum
If you tried adding another hour (which would be $12) that would equal $36 which is over her budget.
which two county libraries charge the same penalty per week
Answer:
where's the rest of the question⁉️
Please only answer if you know the answer thank you.
Answer:
x = - 5;
y = 5;
Step-by-step explanation:
Identify the equation.
y = ( 2 / 3 )x + c;
Substitute a point.
5 = ( 2 / 3 )( - 2 ) + c;
5 = ( - 4 / 3 ) + c;
5 - ( - 4 / 3 ) = c;
5 + ( 4 / 3 ) = c;
19 / 3 = c;
y = ( 2 / 3 )x + ( 19 / 3 );
Substitute point A.
3 = ( 2 / 3 )x + ( 19 / 3 );
3 - ( 19 / 3 ) = ( 2 / 3 )x;
( 9 / 3 ) - ( 19 / 3 ) = ( 2 / 3 )x;
- ( 10 / 3 ) = ( 2 / 3 )x;
- ( 10 / 3 )( 3 / 2 ) = x;
( - 30 / 6 ) = x;
- 5 = x;
x = - 5;
Substitute point B. Use common sense and notice that point B is actually the same as the first point.
y = 5;
Answer:
x = -5
y = 5
Step-by-step explanation:
You could write the equation in the point slope form of a line
y - [tex]y_{1}[/tex] = m( x - [tex]x_{1}[/tex])
Use the slope they gave us 2/3. Use the point they gave us for [tex]x_{1}[/tex] ( -2 ) and [tex]y_{1}[/tex] ( 5)
y -5 = 2/3(x - -2)
y - 5 = 2/3(x + 2) Plug in 3 for y to solve for x
3-5 = 2/3(x + 2)
-2 = 2/3x + 4/3 subtract 4/3 from both sides of the equation
-2 - 4/3 = 2/3x
[tex]\frac{-6}{3}[/tex] - [tex]\frac{4}{3}[/tex] = 2/3x
[tex]\frac{-10}{3}[/tex] = 2/3 x Multiply both sides by [tex]\frac{3}{2}[/tex]
([tex]\frac{3}{2}[/tex])[tex]\frac{-10}{3}[/tex] = ([tex]\frac{3}{2}[/tex])([tex]\frac{2}{3}[/tex]) x
-5 = x
substitute in -2 for x to solve for y
y - 5 = 2/3(x + 2)
y - 5 = 2/3(-2+2)
y - 5 = 2/3(0)
y - 5 = 0 Add 5 to both sides
y = 5
A recipe calls for 3 ⅜ cups of flour. How can you express that mixed number as a fraction?
In Emily's physics class, she had to solve the equation 9 = 12at2 + ut for u. Each step of her work is shown below.
Use the drop-down menus to explain each step.
The equation of u when it is the subject is u = 9/t - 12at
How to determine the solution for the equation for u?From the question, the original equation is given as
9 = 12at2 + ut
Next, we rewrite the equation to show the exponents
This is represented as
9 = 12at² + ut
To solve further, we simply isolate the variable term ut
This is done by subtracting 12at² from both sides of the equation
So, we have the following equation
9 - 12at² = 12at² - 12at² ut
Evaluate the like terms in the equation
So, we have
9 - 12at² = ut
Lastly, divide both sides of the equation by t
So, we have
(9 - 12at²)/t = ut/t
Evaluate the quotients
9/t - 12at = u
Make us the subject
u = 9/t - 12at
Hence, the solution for the equation for u is u = 9/t - 12at
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Hello I just need help with A and B on my homework I was able to complete C
ANSWERS
a) 58
b) 62.2
EXPLANATION
a) The median is the middle value. It separates the data set in two. To find the median we have to put the data in order, from least to greatest:
[tex]44,49,53,54,58,74,74,74,80[/tex]The number of data is odd, this means that the median will be one of the values of the data set and not a mean between two of them. If there are 9 values, the median is the 5th value - so we have 4 values to the left and 4 values to the right.
The first 4 values are 44,49,53,54, so the median is 58.
b) The mean is the sum of all values of the data set divided by the amount of data:
[tex]\bar{x}=\frac{44+49+53+54+58+74+74+74+80}{9}=\frac{560}{9}=62.2222\ldots[/tex]Rounded to one decimal place, the mean is 62.2
Hello! I think I have this correct but want to make sure.
Solution;
y=5x
Explanation;
[tex]\begin{gathered} y\propto x \\ y=kx \\ k=\frac{y}{x} \\ when\text{ x=1 and y=5;} \\ k=\frac{5}{1}=5 \\ Therefore; \\ y=5x \end{gathered}[/tex]Find all the points having an x coordinate of 1 whose distance from the point (-3,-2) is 5
The possible coordinates of the other points are (1, -1) and (5, 1)
How to calculate the coordinates of the points?From the question, we have
Distance = 5 unitsPoints = (-3, -2) and (1, y)Where (1, y) represents the other points
The distance between the points is then calculated using the following distance formula
d = √[(x₁ - x₂)²+ (y₁ - y₂)²]
Where x and y are the coordinates of the two points
Substitute the known values in the above equation
So, we have
d = √[(-3 - 1)²+ (-2 - y)²]
Evaluate
d = √[16+ (-2 - y)²]
The distance is 5 units
So, we have
√[16+ (-2 - y)²] = 5
Square both sides
16+ (-2 - y)² = 25
This gives
(-2 - y)² = 9
Square root of both sides
-2 - y = +/-3
So, we have
y = -2+/-3
Evaluate
y = -1 and y = 5
Hence, the coordinates are (1, -1) and (5, 1)
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PLS HELP!!!
The tables show the cat population on two islands over several years. Describe mathematically, as precisely as you can, how the
cat population on each island is changing.
year
01 2 3
number of cats on Meow Island 2 6 18, 54 162
2 3 4
number of cats on Purr Island 2 6 10 14 18
B I
year
Type your response in the space below.
Type here
01
t
Step-by-step explanation:
Meow island get's their population multiplied by 3 per year
Purr island get's and additional 4 cats per year
The population of cats on each island in the mathematical form is:
Meow island:
f(0) = 2
And,
f(x) = 3f(x - 1)
Where x is the number of years from x = 1, 2, 3 ,,,,
Purr island:
y = 4x + 2
Where x is the number of years from x = 0, 1, 2, 3 ,,,,
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
We will make ordered pair of number of years x and number of cats y as
(x, y).
Meow island:
We see that the number of cats is increasing 3 times the previous number of cats.
So,
f(0) = 2
And,
f(x) = 3f(x - 1)
Where x is the number of years from x = 1, 2, 3 ,,,,
Purr island:
(0, 2), (1, 6), (2, 10), (3, 14) ....
The equation for the table.
y = mx + c
m = (6 - 2) / (2 - 1) = 4/1 = 4
(0, 2) = (x, y)
2 = 4 x 0 + c
c = 2
Now,
y = 4x + 2
Thus,
The population of cats on each island in mathematical form is given above.
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-7/8u = -21 solve for u and simplify your answer as much as possible
Answer:
u = 24
Step-by-step explanation:
-7/8u = -21
Solve for u
Multiply each side by -8/7
-8/7 *-7/8u = -21 *-8/7
u =3*8
u = 24
Answer:
u = 1/24
Write the equation:
–7/8u = –21
Get rid of fraction:
–7/2^3 • u = –21
–7 = ( – (8u) ) 21
Solve:
–7 = –8u + 21
–7 + 8u = –8u + 8u + 21
–7 + 8u = 21
–7 + 7 + 8u = 21 + 7
8u = 21 + 7
8u = 28
u = 1/24
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