We want to find parallel lines to the given lines, such that also meet some given restrictions.
The solutions are:
A) y = 0.5*x - 6
B) two solutions:
y = 0.5*x + 4
y = 0.5*x
Before start answering, a general line is given by:
y = a*x + b
Where a is the slope and b is the y-intercept.
Another line will be parallel this if and only if it has the same slope and a different y-intercept.
A) We want to find a line that is parallel to y = 0.5*x + 10 and that intersects y = -1.5*x
So we want another line with a slope of 0.5, then the correct option is:
y = 0.5*x - 6
How do we know that this intercepts the other line?
Because if two lines have different slopes, then the lines are not parallel, meaning that at some given point the lines intercept.
B) Similarly, now we want a line parallel to:
y = 0.5*x + 10
And that intersects:
y = -1.5*x
The correct options are the ones with slope equal to 0.5, then we have two correct options:
y = 0.5*x + 4
y = 0.5*x
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A farmer has collected data from one of his crops. Suppose the farmer found that the number of seeds, () (in weeks) was
()= t^2/4 seeds per mature plant.
Further, the farmer discovered that only
()=40.56−^2/4+1801.75/^2+188.8/
plants matured to age .
Determine the maximum rate of change of the crop's seed production
The rate of change of the crop's seed production is given by differential of
the function of the number of seeds produced.
The maximum rate of change of the seed production is approximately 117 seeds per week.Reasons:
[tex]\displaystyle \mathrm{The \ number \ of \ seeds \ per \ plant, \ S(t)}= \mathbf{\frac{t^2}{4}}[/tex]
[tex]\displaystyle \mathrm{Plants \ that \ mature \ to \ age \ t, \ P(t)}= \mathbf{40.56- \frac{t^2}{4} + \frac{1,801.75}{t^2} +\frac{188.8}{t}}[/tex]
The number of seeds produced by all the plants, n = S(t) × P(t)
Which gives;
[tex]\displaystyle \mathrm{\ P(t) \times S(t)}= \left(40.56- \frac{t^2}{4} + \frac{1,801.75}{t^2} +\frac{188.8}{t}\right) \times \frac{t^2}{4}[/tex]
[tex]\displaystyle \mathrm{ \left(40.56- \frac{t^2}{4} + \frac{1801.75}{t^2} +\frac{188.8}{t}\right) \cdot\frac{t^2}{4}} = \mathbf{-0.0625\cdot t^4+10.14\cdot t^2 + 47.2 \cdot t + 450.4375}[/tex]
The maximum rate of change is the highest value of the rate of change function.
To find the maximum rate of change of the crops production, the above
function for the number of seeds is differentiated twice. The first
differentiation is to find the rate of change function, and the second
differentiation is to determine the value of t at the maximum rate of change
as follows;
The rate of change of the crop's seed production is given by following function;
[tex]\displaystyle \frac{d}{dt} \left( -0.0625\cdot t^4+10.14\cdot t^2 + 47.2 \cdot t + 450.4375 \right) = -0.25\cdot t^3+ 20.28 \cdot t - 47.2[/tex]
Rate of change function, n'(t) = -0.25·t³ + 20.28·t + 47.2
At the maximum value of the above rate of change function, we have
[tex]\displaystyle \frac{d}{dt} \left( -0.25\cdot t^3+ 20.28 \cdot t - 47.2 \right) = \mathbf{-0.75 \cdot t^2 + 20.28} = 0[/tex]
Which gives
[tex]\displaystyle t^2 = \frac{20.28}{0.75} = \mathbf{27.04}[/tex]
t = √27.04 = 5.2
At the maximum rate of change, the number of weeks, t = 5.2
Plugging in the value of t = 5.2 into the rate of change function gives;
n'(5.2) = -0.25·5.2³ + 20.28·5.2 + 47.2 = 117.504
The maximum rate of change of the crop's seed production is approximately 117 seeds per week.Learn more here:
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HELP NEED ASAP PLS HELP
Answer:
MN = 56
Step-by-step explanation:
This can only be solved if we know the relation of MN to other dimensions of the trapezoid. If we assume MN is a midline (AM=MD, BN=NC), then MN is the average of the base lengths:
MN = (AB +CD)/2
2MN = AB +CD . . . . . multiply by 2
2(12x -4) = 8x +72 . . . fill in the given values for the segment lengths
24x -8 = 8x +72 . . . . . eliminate parentheses
16x = 80 . . . . . . . . . . . add 8-8x
x = 5 . . . . . . . . . . . . . . divide by 16
MN = 12(5) -4 = 56 . . . find the length of MN using its formula
Aden spent $10 on a mug then sold it ,making 20% profit.How much did he sell the mug for?
A.$8
B.$10
C.$11
D.$12
Answer:
12$/D
Step-by-step explanation: 20% of 10 = 2
he spends 10 so -10 then sells for 120% of that which is 12
so, 10+2= 12
Two angles have a difference of 30 degrees. If the greater angle, a, and the smaller angle, b, are complementary, what is the measure of angle a?
Answer:
A=60
Step-by-step explanation:
Complementary means it's 90 degrees
60 and 30 have a 30 degree difference.
The measure of angle a is 60°
What are Complementary Angles?
When the sum of two angles is equal to 90 degrees, they are called complementary angles. For example, 30 degrees and 60 degrees are complementary angles.
Given data ,
The two angles are a and b
a and b are complementary
So , a + b = 90°
The difference of angle a and b is 30°
The greater angle is a and smaller angle is b
So , a - b = 30°
Now , we have two equations
a + b = 90°
a - b = 30°
Adding both equations , we get
2a = 120°
Divide by 2 on both sides , we get
a = 60°
Hence , the measure of angle a is 60°
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Write the quadratic equation whose roots are −4 and 2, and whose leading coefficient is 4.
Answer:
x²+2x-8
leading coefficient is 4
therefore equation is 4x²+x-2
please answer this question if you know please answer it fast
Answer:
(a)Step-by-step explanation:
It has already been answered on the picture.
(a) 1 + 0 = 1 ≠ 0HELP ME PLS WILL MARK BRAINLIEST
Answer:
Step-by-step explanation:
1.) 143.25 - 11.25 = $132
$132 - 22 - 22 - 22 - 22 - 22 - 22 = 132
so 6 people can go
2.) it was 18 miles which stella whent 18 miles from her house to the airport
please mark this as brainlists
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Match the rates with their equivalent unit rates.
(DRAG AND DROP)
Answer:
I have placed it correct answers in the image above
Solve 2x + 6 < 8 or 2x + 8 > 12.
Answer:
x ⋅ ( 2 x ) + 6 < 8 = 2 x 2 + 6 < 8
2 x + 8 > 12 = 2 x 2 + 6 < 8
Step-by-step explanation:
6 times the difference of a number and 3 is more than 24
Answer:
the number is 8
Step-by-step explanation:
8-3=5
6•5=30>24
expression: 6(x-3)>24
In an ice chest there are
10 waters,
6 fruit drinks and 7
sodas. Assume each container is the same size.
If a drink is chosen randomly, then what is the probability that a fruit drink is NOT chosen?
10 more than a number c is 3.
⦁ If the sales tax is 7% on all purchases, how much must you set aside for sales tax on $300? Show your work
Answer:
Step-by-step explanation:
2
Answer:
2
Step-by-step explanation:
2+3/4+2+3/8=what’s the total
Answer:
5 1/8
Step-by-step explanation:
4 + 3/4 + 3/8 =
3/4 + 3/8 = 6/8 + 3/8 = 9/8 = 1 1/8 + 4 = 5 1/8
Suppose that a randomly generated list of numbers from 0 to 9 is being used
to simulate an event that has a probability of success of 20%. Which of these
groups of numbers could represent a success?
Answer:
0, 1
Hope this helps :)
The group {2, 5, 8, 1, 3, 7, 0, 9, 4, 6} contains two "success" numbers (2 and 5) and eight "failure" numbers, so it could represent a success.
What is probability?It is the chance of an event to occur from a total number of outcomes.
The formula for probability is given as:
Probability = Number of required events / Total number of outcomes.
Example:
The probability of getting a head in tossing a coin.
P(H) = 1/2
We have,
To simulate an event that has a probability of success of 20%, we need to randomly generate numbers from 0 to 9 such that there is a 20% chance of getting a "success" number.
Since there are 10 possible numbers to choose from, 20% of them would be 2 "success" numbers.
So, any group of numbers that contains two "success" numbers out of 10 would represent a success.
For example,
The group {2, 5, 8, 1, 3, 7, 0, 9, 4, 6} contains two "success" numbers (2 and 5) and eight "failure" numbers, so it could represent a success.
Other groups with two "success" numbers would also be valid.
Thus,
The group {2, 5, 8, 1, 3, 7, 0, 9, 4, 6} contains two "success" numbers (2 and 5) and eight "failure" numbers, so it could represent a success.
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Solve $2y-18x=-26$ for $y$ .
Answer:
y=-13+9x
Step-by-step explanation:
We can add 18x to both sides:
2y-18x=-26 -> 2y=-26+18x
And then divide by 2:
2y/2=-26/2+18x/2 -> y=-13+9x.
an electronic book has a file size of 2.4 megabytes. what is the file size in megabytes of 16 of theses electronic books?
Answer:
38.4 Megabytes
2.4 x 16 = 38.4
[tex]3x² -10 = -37[/tex]
[tex] {3x}^{2} - 10 = - 37 \\ = > {3x}^{2} = - 37 + 10 \\ = > {3x}^{2} = - 27 \\ = > {x}^{2} = \frac{ - 27}{3} \\ = > {x}^{2} = - 9 \\ = > x = \sqrt{ - 9} \\ = > x = - 3 \: \: or \: \: \: 3[/tex]
Answer:x = -3 or 3
Hope it helps.
Do comment if you have any query.
Phone calls arrive at the reservation desk in a hotel. The arrival rate is constant throughout the day and the arrivals are independent of each other. The average arrival rate is 120 calls per hour. We are interested in the number of incoming calls over a one-minute time period. Using the Poisson probability distribution method compute the probability of receiving exactly 3 calls over a one-minute time period.
a. .20
b. .41
c. 1.41
Answer:
.52
Step-by-step explanation:
sorry
Lucy received 56 of the 180 votes cast for class secretary. How many votes did she receive?
If Lucky received 56 of 180 votes cast, she received 56. The answer is in the question.
What is 200×15x= to?
A truck has a total of b pounds of fruit in n identical boxes. How many
pounds of fruit are in each box?
The product and the square of a number decreased by 5 is 67. Find the number.
Answer: 87
Step-by-step explanation:
Four times a number decreased by 5 is 67.Find the number.
Four times a number decreased by 5 is 67.
4x5=20
X-20=67
X=67+20
X=87
Question 9 of 10
Which of these is a factor in this expression?
5z^4-3+8(y^3+4)
Answer:
its A edge 2021 Unti test
Step-by-step explanation:
Answer:
Step-by-step explanation:
(y^3+7)
Plz help I need help
Please help
what is 6 * 6 * 6 + 9 - 7?
Answer:
218
Step-by-step explanation:
6*6*6 = 216
216+9 = 225
225-7 = 218
someone plz help me plzzzzzz
Answer:
-12
Step-by-step explanation:
To solve for this question, you have to isolate the variable u. To do this, divide both sides by 7/4 to isolate the u. Then your equation should be u= -21 divided by 7/4. This would simplify to -21 times 4/7. This would get you -12. Hope this helps :)
Akira's town had an election last month. 42 people voted in the election and 58 did not vote. What percentage of the people voted?
Answer:
Step-by-step explanation:
Find the total number of people
Total = those voting + those not voting
Total = 42 + 58
Total = 100
Find the % voting
% = voting * 100/ total = 42 * 100 / 100 = 42%
Steve planted 6 dozen tomato plants and harvested an average yield of 104 tomatoes per plant. The next year Steve had a crop of 6,240 tomatoes with the same average yield per plant. How many tomato plants did Steve plant the second year?
Answer:
667680
Step-by-step explanation:
6240 times 104 i think
Answer:
He planted 60 tomato plants, or 5 dozen tomato plants.
Step-by-step explanation:
6 dozen = 6 × 12 = 72
He planted 72 plants and harvested 104 tomatoes per plant.
The next year he had a crop of 6,240 tomatoes, and also got 104 tomatoes per plant.
6,240/104 = 60
He planted 60 tomato plants, or 5 dozen tomato plants.
2.05218617 round 1 decimal place.
Answer:
2.1
Step-by-step explanation:
The digit in the second decimal place is 5, which is more than 4. That means 1 must be added to the digit in the first decimal place when you do the rounding.
2.05... rounds to 2.1
Answer:
2.1
Step-by-step explanation:
The digit in the second decimal place is 5, which is more than 4. That means 1 must be added to the digit in the first decimal place when you do the rounding.
