Answer: 25.5 miles per gallon. 16.8 gallons x 25.5 miles = 428.4 miles
suppose y varies directly with x, and y=6 when x=-3. find x when y=10
The value of the x, when y = 10 by the direct proportional is found as x = -5.
What is defined as the directly proportional?A direct proportion is an arithmetical comparison of two numbers whose ratio is equal to a fixed value. According to the proportion definition, two ratios are in proportion when they are equivalent. The proportions are represented by the symbol " ∝".As per the given question;
y is in the direct variation with x.
This can be written as; y ∝ x.
Or, y = kx
Where, k is proportionality constant.
put the values; y = 6 when x = -3
6 = -3 k
k = -2
Now, the value of x when y = 10.
y = kx ; put the value of y and k
10 = (-2)x
x = -5
Thus, the value of x in direct variation with y = 10 is found as x = -5.
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Ivan was at the beach. He wanted to spend $12 or less on a beach bike rental. The company he chose
to rent from charged an initial fee of $5 and an additional $0.45 per mile he rode.
a. Write an inequality for this situation. Let x represent the number of miles ridden.
b. What is the greatest number of whole miles Ivan can ride without going over his spending
limit?
Using a linear function, it is found that:
a. The inequality for this situation is: 5 + 0.45x ≤ 12.
b. He can ride at most 15 miles without going over the limit.
What is a linear function?A linear function, in slope-intercept format, is modeled according to the following rule:
y = mx + b
In which the coefficients are described as follows:
The coefficient m is the slope of the function, which is the rate of change of the function, that is, the change in y divided by the change in x.The coefficient b is the y-intercept of the function, which is the the value of y when the function crosses the y-axis(x = 0).For the context of this problem, the slope and the intercept are defined as follows:
The slope is the cost per mile, hence m = 0.45.The intercept is the flat cost, the renting fee of b = 5.Hence the cost function, considering x miles, is given as follows:
C(x) = 0.45x + 5.
He wanted to spend $12 or less on a beach bike rental, hence the inequality that models this situation is given by:
C(x) ≤ 12.
5 + 0.45x ≤ 12.
The inequality is solved similarly to an equality, isolating the variable and finding the range of values, hence the solution is found as follows:
0.45x ≤ 7
x ≤ 7/0.45
x ≤ 15.6 miles.
The greatest whole number of miles is of 15 miles, as for 16 miles, the cost would be above $12.
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Rearrange the equation
a= 1/4 b
to make b the subject.
b = 4a is the answer.
How to make b a subject?Given,
a= 1/4 b
To find:
Make b the subject, the given equation
Solution:
Take 4 to the side of a
4a = 1b
Therefore,
b = 4a
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3) Write the equation of the line (in slope-intercept) that passes through (3,10)
a) and is parallel to y = x - 1
b) and is perpendicular to y = x - 1
The Equation of line -
When line is parallel to line y = x - 1 is y = x + 7When line is perpendicular to line y = x - 1 is y = x + 7What is the slope intercept form of a line?
The slope intercept form of a line is given by -
y = mx + c
m is the slope of line
c is the y - intercept
Given is a line that passes through the point (3, 10) and in case [1] is parallel to line y = x - 1 and in case [2] is perpendicular to y = x - 1.
Case 1 - Line is parallel to the line y = x - 1
Assume that the equation of line is -
y = mx + c
Since, the line is parallel, both lines will have same slope and is given by -
m = 1
Since, the line passes through the point (3, 10) we can write -
10 = 1 x 3 + c
c = 7
We can write the equation of line parallel to line y = x - 1 as -
y = x + 7
Case 2- Line is perpendicular to the line y = x - 1 -
Assume that the equation of line is -
y = mx + c
Since, the line is perpendicular, the product of slopes of both lines will be equal to 1. The slope (m) of the line will be -
m x 1 = -1
m = -1
Since, the line passes through the point (3, 10) we can write -
10 = -3 + c
c = 13
We can write the equation of line perpendicular to line y = x - 1 as -
y = - x + 13
Therefore, the equation of line -
When line is parallel to line y = x - 1 is y = x + 7When line is perpendicular to line y = x - 1 is y = x + 7To solve more questions on Straight lines, visit the link below-
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A ball thrown straight upward from a height of 6 ft with an initial velocity of 55 ft per sec has height h(t) feet after t seconds,
where h(t)=-16t+55t+6. What is the ball's average velocity (that is, its average rate of change in height) during the
first second?
The average velocity during the first second is
(Type an integer or a simplified fraction.)
feet per second
Answer:
16t+55t+6t=77. 55-6=49
In a math class with 23 students, a test was given the same day that an assignment
was due. There were 14 students who passed the test and 15 students who completed
the assignment. There were 12 students who passed the test and also completed the
assignment. What is the probability that a student chosen randomly from the class
did not complete the homework?
Answer: 8/23
Step-by-step explanation:
Make a two-way table
Did Assignment Didn't do Assignment
Passed 12 2
Did not pass 3 6
Total 15 8 = 23
2+6=8
8/23
ASAP PLEASE IF YOU CAN
Given the linear equation below, create a table of values to obtain ordered pairs. Plot these ordered pairs to create a linear graph. Based on the graph you created, find three more solutions to the equation.
y equals 3 over 4 x minus 6
The three more solutions to the given linear equation are (2,-9/2), (6,-3/2), and (5,-9/4).
Given equation:-
y = (3/4)x - 6
We have to create a table of values to obtain ordered pairs.
Also, we have to plot these ordered pairs to create a linear graph and based on the graph we have created, we have to find three more solutions to the equation.
Let x = 0
y = 0 - 6 = -6
Ordered pair = (0,-6)
Let y = 0
0 = (3/4)x - 6
6 = (3/4)x
x = 8
Ordered pair = (8,0)
Let x = 4
y = 3 - 6 = -3
Ordered pair = (4,-3)
The graph of these three ordered pairs is attached below.
Based on the graph the other 3 ordered pairs that we can find are (2,-9/2), (6,-3/2), and (5,-9/4).
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Help me with this pleaseeee
Answer:
2, 3
Step-by-step explanation:
[tex]g(x)=\frac{1}{2}(4x+6) \\ \\ =2x+3[/tex]
Given f(x)=√(3x-12)+2 what is the range in set notation? {y|y ∈ R, y ≥ }
The function f(x)=[tex]\sqrt{3x-12} +2[/tex]. The Domain of the function is 4, we can also write {y|y∈R,y≥4}
Given that,
The function f(x)=[tex]\sqrt{3x-12} +2[/tex]
We have to find the range of the function.
Range is nothing but y but in the equation we have x so we find domain.
The domain is the set of inputs that a function will accept is known as the domain of the function in mathematics. It is occasionally indicated by dom(f), where f is function.
More specifically, f:X--->Y the domain of f is X given a function. It should be noted that in contemporary mathematical terminology, a function's domain is a component of its definition rather than a quality.
Take the function
f(x)=[tex]\sqrt{3x-12} +2[/tex]
Now,
3x-12≥0
3x≥12
x≥12/3
x≥4
Therefore, The Domain of the function is 4, we can also write {y|y∈R,y≥4}
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Answer:
2
Step-by-step explanation:
2
Evaluate the Expression when x is -9
When is -9, x^2 is [ ]
(Simplify your answer)
Step-by-step explanation:
that only means we need to put the given values into every place, where the variable is used in the expression.
this is straight forward.
x² for x = -9 means
(-9)² = 81
you remember, a² = a×a.
and when a is negative, this is then the multiplication of a negative number with a negative number, and that result is positive.
so, a square operation always delivers a positive result for real numbers as input, no matter if the input was already positive or negative.
Question 8A: Mr. Sowers wants to purchase expo markers for his classroom. He has a budget of $35. A four pack of markers costs $5.49, including tax. Write and solve an inequality, using x for the variable, to solve for the number of packs of markers Mr. Sowers can purchase. Copy/paste one of the following inequality symbols to help you write your inequality: ≤ < ≥ >
The number of packs of markers that Mr. Sowers can purchase is 6.
How many packs can he buy?The maximum amount that Mr. Sowers can spend is $35. This means that the amount can either by $35 or less than $35. Thus, the inequality sign that would be used is the less than or equal to sign, ≤ .
total amount spent on the packet of markets ≤ budget
(cost of one packet x number of packets) ≤ $35
$5.49x ≤ $35
In order to determine the value of x, divide both sides of the equation by 5.49
x ≤ $35 / 5. 49
x ≤ 6.38
x ≤ 6
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Segment addition and midpoints
In the figure below, B is between A and C, and C Is between B and D. If AC=8, BC=5, and BD=9, find AD.
The line segment AD is 12 units.
How to find the segment AD using midpoint?The midpoint is the middle point of a line segment.
It is equidistant from both endpoints, and it is the centroid both of the segment and of the endpoints.
The midpoint is halfway between the two end points:
Therefore, B is between A and C.
C is between B and D.
Hence,
AC = 8
BC = 5
BD = 9
AD = ?
Therefore,
AD = AB + BC + CD
AB = AC - BC
AB = 8 - 5
AB = 3 units
CD = BD - BC
CD = 9 - 5
CD = 4 units
Therefore,
AD = 3 + 5 + 4
AD = 12 units
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At the beginning of the year, Salma had $35 in savings and saved an additional $8 each week thereafter. Henry started the year with $95 and saved $5 every week. Let SS represent the amount of money Salma has saved tt weeks after the beginning of the year and let HH represent the amount of money Henry has saved tt weeks after the beginning of the year. Write an equation for each situation, in terms of t,t, and determine the number of weeks after the beginning of the year until Salma and Henry have the same amount of money saved.
The number of weeks when Salma and Henry would have the same amount of money is 20 weeks.
How many weeks would they have the same amount?The form of the equations that represent the total amount of money saved is :
Total amount in the account = initial amount in the account + (amount added each week x number of weeks)
SS = $35 + ($8 x tt)
SS = $35 + $8tt
HH = $95 + ($5 x tt)
HH = $95 + $5tt
When they have the same amount in their account, the two equations woud be equal.
HH = SS
$95 + $5tt = $35 + $8tt
$95 - $35 = $8tt - $5tt
$60 = $3tt
tt = $60 / 3
tt = 20 weeks
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Draw the net force arrow on the picture to the left.
Answer:
Step-by-step explanation:
What is the shape of the base of the figure?
16 km
8 km
Answer: rectangle
Step-by-step explanation: brainliest please? i could really use it
Answer:
most likely 16 if its a long object or 8 if its a short one
Step-by-step explanation:
if u provided a graph it could help alot
20 POINTS!
Please Help Me!
What is the equation of the line perpendicular to -2x + 3y = -12 and which passes through the point (2, -5)? Write your answer in slope-intercept form. Show all your work.
Explanation:
the equation of a line in
slope-intercept form
is.
∙
x
y
=
m
x
+
b
where m is the slope and b the y-intercept
rearrange
2
x
−
3
y
=
12
into this form
subtract 2x from both sides
⇒
−
3
y
=
−
2
x
+
12
divide all terms by
−
3
⇒
y
=
2
3
x
−
4
←
in standard form
with
m
=
2
3
given a line with slope m then the slope of a line
perpendicular to it is
∙
x
m
perpendicular
=
−
1
m
⇒
m
perpendicular
=
−
1
2
3
=
−
3
2
⇒
y
=
−
3
2
x
+
b
←
is the partial equation
to find b substitute
(
2
,
6
)
into the partial equation
6
=
−
3
+
b
⇒
b
=
6
+
3
=
9
⇒
y
=
−
3
2
x
+
9
←
equation of perpendicular line
Lucy earns $15.75 per hour. Last week she worked 25 hours. What is her gross pay?
Lance has a yearly salary of $52,300 and pays 21% in taxes. Answer the following
a. How much does he pay in taxes?
b. What is his net pay?
c. If he receives two paychecks a month, how much will each paycheck be?
If Lucy earns $15.75 per hour. Last week she worked 25 hours her gross pay is $393.75 . If Lance has a yearly salary of $52,300 and pays 21% in taxes her taxed amount is $10,983, net pay is $41,317 and paycheck is $2,179.
Gross pay1. Gross pay
Using this formula to determine the gross pay
Gross pay = Amount earn per hour × Number of hours worked
Let plug in the formula
Gross pay = $15.75 per hour × 25 hours
Gross pay = $393.75
2a. Taxed amount
Amount in Tax = Salary × Tax percentage
Amount in taxes = $52,300 × 21%
Amount in taxes = $10,983
2b. Net pay
Net pay = Gross - Deduction
Net pay = $52,300 - $10,983
Net pay = $41,317
2c. Paycheck
Paycheck = $52,300 / 24 months
Paycheck = $2,179 per paycheck
Therefore we can conclude that the her gross pay is $393.75
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Timmy is working with 2 sets of numbers.
Set A has all the odd number from 1-10.
Set B has all the even numbers from 2-20.
What is the ratio that represents the prime
numbers in Set A to the prime numbers in Set B?
(HINT: Think about what prime numbers are.)
Answer:
there's no ratio, or maybe u can help me out
Question
Refer to the Newsela article, "Doctoral Student Played a Big Part in First Black Hole Photo."
How does Bouman contribute to taking the first photograph of a black hole?
Responses
Bouman is the first person to suggest that black holes exist in space.
Bouman invents a telescope that can gather images taken by eight telescopes located around the world.
She and her team create an algorithm that makes it possible to collect data and combine it into one image.
Her TED talks on black holes inspire other scientists to figure out how to photograph them.
Bouman contributed to taking the first photograph of a black hole as she and her team created an algorithm that makes it possible to collect data and combine it into one image.
What facts are drawn from Newsela article?The article highlighted the importance of Katie Bouman in leading her team who created a computer software capable of using an algorithm that analyzes data and creates an image based on it. Its elaboration took about two years to complete but the results were very promising and promoted a great advance for science.
In conclusion, Bouman and the team were able to develop series of algorithms that converted telescopic data into the historic photo shared by the world's media.
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HELPP ONBB- I just realized this is due today!!
The rate of change (m) = 9
The starting number (b) = 100
The equation is: y = 9x + 100
(0, 100) is the ordered pair for the starting number.
See the image for the graph of y = 9x + 100.
How to Create and Graph the Equation of a Line?To create the equation of a line, we need to determine the following:
Y-intercept/starting value = b
Slope of the line/rate of change = m
The ordered pair of the y-intercept or starting value is represented as (0, b), where b is the value of y on the y-axis where the line intercepts the y-axis and x = 0 at this point.
These values can be substituted into y = mx + b, which represents the equation of the line in slope-intercept form.
From the information given, we have:
Y-intercept/starting value (b) = 100
Slope of the line/rate of change (m) = 9
To write the equation of the line, substitute m = 9 and b = 100 into y = mx + b:
y = 9x + 100
The ordered pair for the starting number would be: (0, 100).
The image below shows the graph of y = 9x + 100.
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4x^-x/x^3-2 how much
Answer:
4x^-x-1
Step-by-step explanation:
4x^-x/x^3-2
= 4x^-x/x
= 4x^-x-1
you’ve asked for a survey of your property and the surveyor has just sent you a drawing of your property boundary. you show it to your neighbor and he says that the boundary between your two properties is wrong. he says his legal description says that that boundary bears n49°31’56.37""w at 363.591’. he says you shouldn’t pay the surveyor and get him back out to re-survey that line. who is right?
"Seven Year Rule," which is derived from Section 157(4) of the Planning and Development Act 2000, is not the same as this.
What does the seven-year time limit mean?
The so-called "Seven Year Rule," which is derived from Section 157(4) of the Planning and Development Act 2000, is not the same as this. This indicates that once seven years have passed after the start of the development, local authorities cannot issue enforcement notices for an unauthorized development.It is time to speak with a lawyer or the organization that insured your title if there is a sizable discrepancy between where two deeds set a property border. It's possible that a mistake was made when drafting one of the deeds. To try to pinpoint the time the issue happened, someone may need to conduct research on both attributes. The mistake can affect multiple previous landowners.Remember that the majority of surveys indicate the property lines on the deed. Usually, the poll doesn't directly state that a certain action is improper. Ideally, the position of the property line is agreed upon in both documents. Both properties likely once belonged to a bigger tract.Learn more about Seven year rule'
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Draw the graph of f(x)=[[x - 4]] - 2
Answer:
See attachment.
Step-by-step explanation:
Given absolute value function:
[tex]f(x)=|x-4|-2[/tex]
The parent absolute value function is f(x) = |x|.
Graph of the parent absolute value function:
Vertex at (0, 0)|y| = -x if x ≤ 0|y| = x if x ≥ 0Translations
[tex]\textsf{For $a > 0$}:[/tex]
[tex]f(x+a) \implies f(x) \: \textsf{translated $a$ units left}.[/tex]
[tex]f(x-a) \implies f(x) \: \textsf{translated $a$ units right}.[/tex]
[tex]f(x)+a \implies f(x) \: \textsf{translated $a$ units up}.[/tex]
[tex]f(x)-a \implies f(x) \: \textsf{translated $a$ units down}.[/tex]
The graph of the given function is a transformation of the parent function by:
Translation of 4 units right.Translation of 2 units down.Therefore, the vertex of the given function is (4, -2).
Find two further points on the graph by inputting x-values either side of the x-value of the vertex into the given function:
[tex]\begin{aligned}\implies f(8)&=|8-4|-2\\&=|4|-2\\&=4-2\\&=2\end{aligned}[/tex]
[tex]\begin{aligned}\implies f(0)&=|0-4|-2\\&=|-4|-2\\&=4-2\\&=2\end{aligned}[/tex]
To draw the graph of the given function:
Plot the vertex (4, -2).Draw a straight line from the vertex through point (8, 2).Draw a straight line from the vertex through point (0, 2).Answer these question
Hannah needs to build two wall, One has a height of 1024 feet and the other of 672 feet. If hannah has to use bricks of equal sizes for both wall, what is the biggest size of each brick she can use. ( Answer in feet)
There are now x cans stacked on a shelf that hold 36 cans when full, If 4 of these cans were removed, the shelf would be half full. Find x
1. The biggest size of each brick that Hannah can be able to use is 32.
2. The value of x when there are now x cans stacked on a shelf that hold 36 cans when full is 22 cans.
How to illustrate the information?From the information, Hannah needs to build two wall, one has a height of 1024 feet and the other of 672 feet and she has to use bricks of equal sizes for both wall. It should be noted that this implies that we've to calculate the highest common factor for 672 and 1024. This is 32.
2. The value of x will be:
= (36/2) + 4
= 18 + 4
= 22
Therefore, x is 22. This means that there are 22 cans.
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Solve for x: 4x + 1/2 (2x+4) > 12
a. x > 14/5
b. x < 14/5
c. x > 2
d. x < 2
Answer:
c. x > 2.
Step-by-step explanation:
4x + 1/2 (2x+4) > 12
4x + x + 2 > 12
5x > 10
x > 2.
prove that (a - b)2 = (b - a)2
Answer:
Step-by-step explanation:
(a - b)² =
(a - b)(a - b) =
[(- 1)(b - a)] × [(- 1)(b - a)] =
(- 1)(- 1)(b - a)(b - a) =
(b - a)²
Two cars leave from a place at the same time they travel in opposite directions one at 62 KM per hour the other at 48 KM per hour how long will it take before they are 550 KM apart
If two cars leaves from a place at the same time they travel in opposite directions and the speed of the first and second cars are 62 km per hour and 48 km per hours respectively , 5 hours will take before they are 550 km apart
The speed of the first car=62 km per hour
The speed of the second car=48 km per hour
Two cars leave from a place at the same time they travel in opposite directions
The relative speed of the car = Speed of the first car - (- Speed of the second car )
=62-(-48)
=110 km per hour
Time take = Distance between the two cars / Relative speed of the two care
=550/110
=5 hours
Hence, if two cars leaves from a place at the same time they travel in opposite directions one at 62 km per hour the other at 48 km per hour, 5 hours will take before they are 550 km apart
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7
The curve with equation y=pr²-4px-5p, where p is a constant does not intersect the line with
equation y=2x-12.
(a) Show that 9p²-8p+1 <0
(b) Find the set of possible values for p.
The set of possible values for "p" is ((4-√7)/9, (4+√7)/9).
The equation of the line is :y = 2x - 12The equation of the curve is :y = px² - 4px - 5pUsing the above two equations, we get the relationship that is given below :px² - 4px - 5p = 2x - 12px² - (4p+2)x - 5p+12 = 0(a) We are given that the curve and the line don't intersect, so the equation should not have a root.For the quadratic to not have a real solution, the discriminant is negative.b² - 4ac < 0[-(4p+2)]² - 4(p)(-5p+12) < 0(4p+2)² + 4(p)(5p-12) < 016p² + 4 + 16p + 20p² - 48p < 036p² - 32p + 4 < 09p² - 8p + 1 < 0(b) 9p² - 8p + 1 < 09p² - 8p + 1 = 0p = (4±√7)/9For the inequality to satisfy:p∈((4-√7)/9, (4+√7)/9)To learn more about equations, visit :
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[tex]1/1+\sqrt2+1/\sqrt2+\sqrt3+1/\sqrt3+\sqrt4[/tex]
Please help me on this question!