Billy wants to live in the area defined by y < 3x − 6. Explain how you can identify the houses in which Billy is interested in living. (2 points)
Answers
to graph an inequality, you pretty much first off, need to graph the "equality" or equation, so for y < 3x − 6, first off, graph the line y = 3x − 6.
and then you do a "true" or "false" check.
now, if you look at the line below, it splits the grid in two sections, so, let's check a point in either section, if one is false, the other is true and the other way around.
so, let's check the region on the left-hand-side, hmmmm say point 0,0, the origin.
y < 3x - 6
y = 0, x = 0 thus
0 < 3(0) - 6
0 < -6 <--- now, is that really true? is 0 lesser than -6? not quite, is false.
recall that on the negative side, the closer to 0, the larger the value, so -1 is much larger than -1,000,000.
because the point 0,0 yielded a false inequality, that region is the "false region" and thus not shaded, therefore, the other side must be the "true region", and thus we shade that then.
we can run a quick check on that btw, say on point 4,4
y =4, x = 4 thus
4 < 3(4) - 6
4 < 12 - 6
4 < 8 <---- yeap, is true, 4 is lesser/smaller than 8.
hmm ohh yes, the line needs to be dashed for a < or >, because it "has that boundary but it does not include it", unlike ⩽ and ⩾, which is a solid line, because it has that boundary and it includes it too.
Related Questions
A northbound train and a southbound train meet each other on parallel tracks heading in opposite directions. The northbound train travels 4 miles per hour faster than the southbound train. After 2.5 hours, they are 330 miles apart. At what speeds are the two trains traveling?
Answers
if, the southbound train is going at a speed of say " r " mph, since we know that the northbound one is going faster by 4 miles, than is really going at " r + 4 " mph then.
now, we know in 2.5 hours, they're 330 miles from each other, thus the southbound train has been rolling for 2.5 hours, and the northbound train has also been rolling for 2.5 hours.
if the northbound train has covered on those 2.5 hours say " d " miles, then the southbound train has covered the slack, or " 330 - d ".
[tex]\bf \begin{array}{lccclll} &\stackrel{miles}{distance}&\stackrel{mph}{rate}&\stackrel{hours}{t}\\ &------&------&------\\ Northbound&d&r+4&2.5\\ Southbound&330-d&r&2.5 \end{array} \\\\\\ \begin{cases} \boxed{d}=2.5(r+4)\\ 330-d=2.5r\\ ----------\\ 330-\boxed{2.5(r+4)}=2.5r \end{cases} \\\\\\ 330-2.5r-10=2.5r\implies 320=5r\implies \cfrac{320}{5}=r\implies 64=r[/tex]
how fast is the northbound going? well, r + 4.
Consider the exponential function f(x) = 3 and its graph. Which statements are true for this function and graph? Check all that apply. The initial value of the function is . The growth value of the function is . The function shows exponential decay. The function is a stretch of the function f(x) = . The function is a shrink of the function f(x) = 3x. One point on the graph is (3, 0).
Answers
The function shows exponential growth a stretch of the function f(x) = (1/3)^x .
What are exponential functions?When the expression of a function is such that it involves the input to be present as the exponent (power) of some constant, then such a function is called an exponential function. Their usual form is specified below. They are written in several equivalent forms.
Given that the exponential function f(x) = 3
The initial value of the function is 2.
The base of the function is 3.
When the intial value is where x=0
where x=0, the value of f(0)=3
The growth is 1/3 but it is decay, that might be correct, or not because it is decay.
It is a stretch of the function f(x)=(1/3) power of x
when x=3, then f(3)=1/9
The function shows exponential growth a stretch of the function f(x) = [tex](1/3)^x[/tex].
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How to solve -5 3/14 to the thousandths place?? Please help
Answers
[tex]\bf \stackrel{mixed}{-5\frac{3}{14}}\implies -\cfrac{5\cdot 14+3}{14}\implies \stackrel{improper}{-\cfrac{73}{14}}\implies -73\div 14\approx -5.21428571 \\\\\\ -5.\stackrel{tenth}{2}~\stackrel{hundreth}{1}~\stackrel{thousandth}{4}[/tex]
Is y=7x+2 x+7y=8 parallel, perpendicular, or neither?
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y = 7x + 2
y = -(1/7) x + 8
product of their slopes is 7 * -1/7 = -1 so they are perpendicular
Which triangle has 0 reflections of symmetry
Answers
Answer:
The answer would be option A the scalene triangle
Answer:
The first triangle, or, A !!
Step-by-step explanation:
Using sum or difference formulas, find the exact value of sin(165∘)
Express your answer in the form
sin(165∘)=√a(√b−1)/4 for some numbers a and b
Answers
We have a = 2 and b = 3.
To find the exact value of sin(165°) using sum or difference formulas, we notice that 165° can be expressed as the sum of two angles whose sine and cosine values we know exactly, for example, 120° and 45°. The sum formula for sine is sin(A + B) = sin(A)cos(B) + cos(A)sin(B).
Therefore, sin(165°) = sin(120° + 45°) = sin(120°)cos(45°) + cos(120°)sin(45°).
From here, we use the known values:
sin(120°) = sin(180° - 60°) = sin(60°) = √3/2
cos(45°) = √2/2
cos(120°) = cos(180° - 60°) = -cos(60°) = -1/2
sin(45°) = √2/2
Plugging these values into our formula gives:
sin(165°) = ( √3/2)(√2/2) + (-1/2)(√2/2) = (√6 - √2)/4
This fraction can be rewritten to match the given form by factoring out √2 in the numerator:
sin(165°) = √2(√3 - 1)/4
Hence, in the form sin(165°) = √a(√b - 1)/4, we have a = 2 and b = 3.
7/6 - 4/3n = -3/2n + 2(n + 3/2)
Answers
Holland added three decimals that made a sum of 2. One of the decimals was 0.34. What are two other decimals Holland could have used to make a sum of 2
Answers
To solve, 1st subtract 0.34 on both sides to get 2x = 1.66. Now divide by 2 on both sides to get x = 0.83.
So your decimals are 0.34, 0.83, and 0.83
Answer:
In general the two other decimals are x and y that satisfy x + y = 1.66 where x ≤ .99 and y ≤ .99
One particular pair would be x = 0.99 and y = 0.67
Step-by-step explanation:
If Holland added three decimals that made a sum of 2 and one of them was 0.34, we are going to name x and y to the other 2 decimals.
We are going to write the equation:
[tex]0.34 + x +y= 2\\x+y=2-0.34\\x+y = 1.66[/tex]
So we have that both the other numbers have to sum 1.66, however, we know both numbers are decimals so neither one of them can be greater than 1.
So this problem has many answers and the answers would be all the numbers that satisfy x + y = 1.66 where x ≤ .99 and y ≤ .99
For example, if x = 0.99, y would be:
y = 1.66 -0.99 = 0.67.
And our pair of numbers would be 0.99 and 0.67.
If x = .80, y would bey = 1.66 - 0.80 = 0.86
And our pair of numbers would be 0.80 and 0.86
This way, we can find more than 1 answer for the other two decimals.
Chris plans to mulch the Border surrounding a rectangular Garden in his backyard if the length of L of the garden (exculding its border) is 3 more than twice its width w and the width of the border is 1/4w which function repersents tje area A to be mulched in terms of w?
Answers
Width of the garden = w
Length of the garden = 2w+3
Width of the entire plot = w + 0.5w = 1.5w
Length of the entire plot = (2w + 3) 0.5w = 2.5w + 3
Area of the garden = w (2w + 3)
Area of the entire plot = 1.5w (2.5w + 3)
Area of the garden = 2w² + 3w
Area of the entire plot = 3.75w² + 4.5w
Area of border = area of the entire plot - area of the garden
= 3.75w² + 4.5w - (2w² + 3w)
Area of the border = 3.75w² + 4.5w - 2w² - 3w
Area of the border = 1.75w² + 1.5w
Find the volume of the solid region. the solid between the planes z = 3x + 2y + 1 and z = x + y, and above the triangle with vertices (1, 0, 0), (2, 2, 0), and (0, 1, 0) in the xy-plane.
Answers
The volume of the solid region. the solid between the planes z = 3x + 2y + 1 and z = x + y, and above the triangle with vertices (1, 0, 0), (2, 2, 0), and (0, 1, 0) in the xy-plane is 6 cubic unit.
What is volume?It is defined as a three-dimensional space enclosed by an object or thing.
It is given that
The solid between the planes z = 3x + 2y + 1 and z = x + y, and above the
triangle with vertices (1, 0, 0), (2, 2, 0), and (0, 1, 0) in the xy-plane.
r(u) = (1, 2)
r(v) = (-2, -1)
|r(u)xr(v)| = 3
The volume of the solid:
∬S(3x + 2y + 1 − x − y)ds = ∫₀¹ ∫(u, 0)(2x + y +1)3 dv du
After solving:
= 3(4/3 - 5 /6 + 3/2)
= 6
Thus, the volume of the solid region. the solid between the planes z = 3x + 2y + 1 and z = x + y, and above the triangle with vertices (1, 0, 0), (2, 2, 0), and (0, 1, 0) in the xy-plane is 6 cubic unit.
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Final answer:
The volume of the solid region between the planes z = 3x + 2y + 1 and z = x + y, above the triangular region in the xy-plane, can be found using a double integral over the triangular area defined by vertices (1, 0, 0), (2, 2, 0), and (0, 1, 0).
Explanation:
To find the volume of the solid region between the planes z = 3x + 2y + 1 and z = x + y, and above the triangular region in the xy-plane, we can use a double integral over the triangular region. The volume is given by the difference between the two planes integrated over the area of the triangle formed by the vertices (1, 0, 0), (2, 2, 0), and (0, 1, 0).
First, define the vertices of the triangle in the xy-plane: A(1, 0), B(2, 2), and C(0, 1).
Second, find the equations of the lines forming the sides of the triangle, which helps in defining the limits of the integral.
Lastly, set up the double integral:
∫∫ (3x + 2y + 1) - (x + y) dA,
after solving, we get volume = 6
where dA is the differential area element in the xy-plane, and the limits of integration are determined by the triangular region.
The integration can be simplified by determining a suitable ordering for dx and dy, often choosing to integrate in x first and then y, or vice versa, based on the geometry of the triangle. The exact bounds for x and y need to be worked out from the equations of the lines defining the triangle's edges.
The result of this integral will give the volume of the solid region bounded by the two planes and above the triangle.
The current (I) in an electrical conductor varies inversely as the resistance (r) of the conductor. The current is 2 amperes when the resistance is 960 ohms. What is the current when the resistance is 480 ohms?
Answers
[tex]\frac{2}{1} = \frac{k}{960} \\k=2\cdot960=1920[/tex].
Since we know the data to find the current when the resistance is 480 Ohms [tex]\Rightarrow[/tex] [tex]I=\frac{k}{r}=\frac{1920}{480}=4 \ amperes[/tex].
Brenda can deliver 644 newspapers in 7 hours. How many newspapers can Brenda deliver in 9 hours?
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92 per day
92x 9= 828
Answer is 828 newspapers
That gives you 92.
Times that by 2 and get 184, then add 644 to that.
That equals 828, and that is your answer.
Brenda can deliver 828 newspapers in 9 hours.
Hope this helps
If twice a number decreased by 5 and the result is multiplied by 4, the result is 36. find the number
Answers
(2x-5)4=36
2x-5=9 <----- divide by 4
2x=14 <----- add 5
x=7 <----- divide by 2
a diamond's density is 3.2 g/cm3
determine the volume of a diamond that has a mass of 1 g
Answers
________________________________________________________
1 g * (1 cm³ / 3.2g) = __?___ cm³ ;
The units of "g" cancel ;
and we have: (1/3.2) cm³ ;
= (1 ÷ 3.2) cm³ ;
= 0.3125 cm³ ; or; write as: 13/40 cm³ .
_____________________________________
which function is an even function?
Answers
All the functions in the problem are constant functions, because no x is involved.
For example, consider the first function: [tex]f(x)=sin(-3 \pi)[/tex],
[tex]sin(-3 \pi )[/tex] is just a constant value.( it is actually equal to 0)
Thus for any x, f(x) = 0 and f(-x) =0
This can be said for all constant functions: all of them are even functions.
Answer: all
Consider the linear function that is represented by the equation y=-10x+6 and the linear function that is represented by the equation y-36=8(x-4). Which statement is correct regarding their slopes and y-intercepts?
a. The function that is represented by the equation y=-10x+6 has a steeper slope and a greater y-intercept.
b. The function that is represented by the equation y=-10x+6 has a steeper slope, and the function that is represented by the equation y-36=8(x-4) has a greater y-intercept.
c. The function that is represented by the equation y-36=8(x-4) has a steeper slope, and the function that is represented by the equation y=-10x+6 has a greater y-intercept.
d. The function that is represented by the equation y-36=8(x-4) has a steeper slope and a greater y-intercept.
Answers
This is about understanding slopes.
Option A is correct.
We are given two linear functions which are;y = -10x + 6 - - - (eq 1)
y - 36 = 8(x - 4) - - - (eq 2)
Formula for straight line equation is;y = mx + c
Where m is slope and c is the y intercept.
Let's expand eq 2 to be in the form of y = mx + c
Thus;
>>y - 36 = 8(x - 4)
>> y - 36 = 8x - 32
>> y = 8x - 32 + 36
>> y = 8x + 4 - - - (eq 3)
Thus, slope of eq 1 is -10 and y-intercept is 6.
Similarly, slope of eq 3 is 8 and y-intercept is 4.
This means y = -10x + 6 has a greater y-intercept than y - 36 = 8(x - 4).
Also, the slope in y - 36 = 8(x - 4) which is 8 will slope to the right while the slope of y = -10x + 6 which is -10 will slope to the left. This means that line represented by y = -10x + 6 has a steeper slope.
This is because the higher the slope, the steeper the line.
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After rewriting both equations in slope-intercept form, we find that the function y = -10x + 6 has a steeper slope and the function y - 36 = 8(x - 4) has a greater y-intercept, making option (b) the correct answer.
The question involves comparing the slopes and y-intercepts of two linear functions, represented by the equations y = -10x + 6 and y - 36 = 8(x - 4). To compare them, we need to write both equations in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.
The first equation, y = -10x + 6, is already in slope-intercept form, with a slope of -10 and a y-intercept of 6. For the second equation, y - 36 = 8(x - 4), we first distribute the 8 to get y - 36 = 8x - 32 and then add 36 to both sides to get the slope-intercept form, y = 8x + 4, which has a slope of 8 and a y-intercept of 4.
Comparing the slopes, -10 for the first equation and 8 for the second, we see that the first equation has a steeper slope because -10 has a greater magnitude than 8. Comparing the y-intercepts, 6 for the first equation and 4 for the second, the first equation has a greater y-intercept. Therefore, the correct statement regarding their slopes and y-intercepts is (b) The function that is represented by the equation y = -10x + 6 has a steeper slope and the function that is represented by the equation y - 36 = 8(x - 4) has a greater y-intercept.
Suppose you are taking the bus home, and can take either the 51 or the 82. you know that the 82 will arrive in exactly 10 minutes, but because the 51 is unreliable, you suspect that the amount of time until it arrives is uniformly distributed between 0 and 30 minutes. you take the first bus that arrives. let t be the number of minutes you wait until you board a bus. find e[t].
Answers
Final answer:
The expected waiting time for a bus, E[t], is 8.33 minutes, which is calculated considering the possibility of either bus 51, which has a uniform arrival time between 0 to 30 minutes, or bus 82, which arrives in exactly 10 minutes.
Explanation:
The problem you are dealing with involves finding the expected waiting time, E[t], for either bus 51 or bus 82 to arrive. The expected value of a uniformly distributed random variable on an interval [a, b] is given by the formula (a + b)/2. However, we need to account for the fact that if bus 82 arrives in exactly 10 minutes, then if the 51 bus hasn't arrived by then, you will take the 82 bus.
To compute E[t], if the 51 bus arrives within the first 10 minutes, the expected waiting time is the average of 0 and 10 minutes, which is 5 minutes. If the 51 bus does not arrive within 10 minutes, you will take the 82 bus at exactly 10 minutes. Therefore, the expectation must only account for the time if the 51 bus arrives before the 82. This gives us:
The probability that the 51 bus arrives in the first 10 minutes is 10/30 = 1/3.
The expected waiting time if 51 arrives in the first 10 minutes is 5 minutes.
If the 51 bus does not arrive within 10 minutes, you'll wait exactly 10 minutes for the 82 bus.
So, E[t] = (1/3) * 5 minutes + (2/3) * 10 minutes = (5 + 20)/3 = 25/3 minutes.
Therefore, the expected waiting time E[t] is 8.33 minutes (rounded to two decimal places).
Mohammad would like to graph the line that represents the total number of baseball cards he will have collected, T, after m months, given that he buys 5 cards each month and he started with no cards. He would like the graph to show the number of cards after 6 and 12 months. Select from the drop-down menus to correctly complete each statement. To best show this information, the scale for the T-axis of his graph should go from 0 to at least , and the m-axis of his graph should go from 0 to at least .
Answers
Solution:
Number of Baseball cards bought by Mohammad each month = 5
As number of baseball cards is represented by T , which are
T = 0,5,10,15,20,25,30,35,40,45,50,55,60 →→ Y axis
Number of months(m) from which Mohammad started buying cards is given as
m = 0,1,2,3,4,5,6,7,8,9,10,11,12 →→ X axis
The given information represented in equation form
T = 5 m
This is a equation of line in two variable passing through origin.
Slope of line = 5 =Amount of baseball card bought each month
Number of cards bought after 6 months = 5 × 6=30
Number of cards bought after 12 months = 5 ×12 =60
Graph is depicted below.
The scale for the T-axis of his graph should go from 0 to at least 60 , and the m-axis of his graph should go from 0 to at least 12 .
convert y=2x-7 to slope intercept form
Answers
So y = 2x - 7
A child types the letters q, w, e, r, t, y, randomly producing 1000 letters in all. what is the expected number of times that the sequence qqqq appears, counting overlaps
Answers
1000/1296 is less than 1.
Expected number of times qqqq (or any given 4-letter sequence) will appear in 1000 letters is 0.
The expected number of times the sequence 'qqqq' appears in 1000 random typings of 6 different letters is approximately 0.769 times.
Explanation:
This problem falls under the category of discrete probability in mathematics. The child randomly types one of 6 different letters.
Therefore, the probability of typing any one specific letter, such as 'q', is 1/6. The sequence 'qqqq' is a sequence of 4 specific letters. Thus, the probability of typing this sequence at any given point is (1/6)^4 or 1/1296. To find the expected number of times the sequence 'qqqq' will appear in 1000 typed letters, we multiply the probability of the event by the number of attempts. However, because 'qqqq' is a sequence of 4 letters, our attempts are based on 4-letter sequences and not individual letters. So, instead of 1000 letters, we have 1000 - 4 + 1 = 997 possible 4-letter sequences in 1000 letters.The expected number of times the sequence 'qqqq' will appear is then 997 * (1/1296) which is approximately 0.769. In simple words, we would expect the sequence 'qqqq' to occur around 0.769 times or less than once in 1000 random typings of the 6 different letters.Learn more about Expected Value here:https://brainly.com/question/35639289
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It is important to re-evaluate financial goals periodically. In which of the following situations would it be necessary to change an existing financial goal?
a. You fell sharply behind your expected schedule with regard to saving.
b. You recovered from an unexpected expense and are rattled that you did not see it coming.
c. You married, and your spouse has a similar financial goal.
d. You came across unexpected income.
Please select the best answer from the choices provided
A
B
C
D
Answers
You're financial goal and planning should be designed to fulfill a realistic expectation on your financial situation somewhere in the future.
When you're behind the schedule, you should either bring down the threshold for your financial goals to make it more realistic to achieve or find another source of income so your target could still be fulfilled even though you have to make additional sacrifice
Which equation represents a direct variation?
Answers
Hope this helps!
Answer:
a y=.5x
Step-by-step explanation:
please dont look at my name
**I really need help on this! Please answer!*
The table shows the scoring system for quarterbacks in Jeremy's fantasy football league. In one game, Jeremy's quarterback had 2 touchdowns passes, 16 complete passes, 7 incomplete passes, and 2 interceptions. How many total points did Jeremy's quarterback score?
**QUARTERBACK SCORING**
Touchdown pass - 6
Complete pass - 0.5
Incomplete pass - -0.5
Interception - -1.5
Answers
The total number of points = 13.5 points
What is the total amount of points gained?
We are given the scoring method as:
Touchdown pass: 6
Complete pass : 0.5
Incomplete pass : -0.5
Interception : -1.5
Now, we are told that Jeremy's quarterback had the following:
2 touchdowns passes,
16 complete passes,
7 incomplete passes,
2 interceptions.
Thus:
Total points = (2 * 6) + (0.5 * 16) + (-0.5 * 7) + (-1.5 * 2)
Total points = 13.5 points
Someone please help me!
Answers
check the picture below.
baby sister took nap for 2 hours and 22 minutes and 1 hour and 35 minutes yesterday. how many more minutes did she sleep yesterday than today
Answers
what is the basic ratio for 30:42
Answers
The lowest form for that is 5/7. Hope that helped. Good luck
The basic ratio of 30:42 is 5:7. This was found by simplifying the ratio to its lowest terms, which is done by dividing both sides of the ratio by the largest number that can evenly divide both numbers, the greatest common factor (GCF).
Explanation:The basic ratio of 30:42 is found by simplifying the ratio to its lowest terms. To do this, find the greatest common factor (GCF) of the two terms, which is the largest number that can evenly divide both numbers. In this case, the GCF of 30 and 42 is 6. Therefore, by dividing both sides of the ratio by 6, we get the simplified ratio: 5:7. So, the basic ratio for 30:42 is 5:7.
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describe how you would Use the distributive property to simplify 39 * 5
Answers
~PutarPotato
This graph shows a portion of an even function. Use the graph to complete the table of values.
Answers
1
3
3
all you really have to look at is how the graph is set up and then you have the answers like up top
1, 1, 3, 3 - I just did it on e2020 and got it correct
Evaluate the series 50 + 10 + 2 + . . .
Answers
[tex]r=\dfrac{a_2}{a_1}=\dfrac{10}{50}=\dfrac{1}{5}[/tex]
so:
[tex]S=50+10+2+\ldots=\dfrac{a_1}{1-r}=\dfrac{50}{1-\frac{1}{5}}=\dfrac{50}{\frac{4}{5}}=\dfrac{50\cdot5}{4}=\dfrac{250}{4}=\boxed{62.5}[/tex]
On a trip to the beach, you travel 200miles in 300 minutes. How fast did you travel?