Ms. Lady works-out with Ms. Beetle; her average crawling time has increased to 4 feet per minute, while Ms. Beetle, who is used to eating Hot Cheetos and watching TV, averages 2.5 feet per minute. While at Senn's Elm Tree-house, the three decide to experiment with linear equations. The objective is to end up at the Rose Bush at the same time. Senn still averages 5 feet per minute. How much of a head start does he need to give each of his friends in order for their function rules to intersect at 92 feet (the rose bush). What is the equation for each bug which makes their experiment successful? Create a table and graph representing the situation.
Answers
Answer:
Senn needs to give Ms. Lady 4.6 minutes head start
Senn needs to give Ms. Beetle 18.4 minutes head start
The equation for each bug are;
For Senn, the equation for the experiment is 5 × t₁ = 92 feet
For Ms. Lady, the equation for the experiment is 4 × (t₁ + 4.6) = 92 feet
For Ms. Beetle , the equation for the experiment is 4 × (t₁ + 18.4) = 92 feet
Please find attached the required graph and table of values
Step-by-step explanation:
The given parameters are;
The average crawling time of Ms. Lady = 4 feet per minute
The average crawling time of Ms. Beetle = 2.5 feet per minute
The average crawling time of Senn = 5 feet per minute
The distance to the rose bush = 92 feet
Therefore, we have;
The time, t, duration for Senn to arrive at the Rose bush is given by the following relation,
Time, t = Distance, d/(Speed, s)
Given that the speed of the bugs is equal to their average crawling time, we have
For Senn
Time, t = 92/(5 ft/Min) = 18.4 minutes
For, Ms. Lady
Time, t = 92/(4 ft/Min) = 23 minutes
For, Ms. Beetle
t = 92/(2.5 ft/Min) = 36.8 minutes
Therefore;
Senn needs to give Ms. Lady 23 - 18.4 = 4.6 minutes head start
Similarly, Senn needs to give Ms. Beetle 36.8 - 18.4 = 18.4 minutes head start
The equation for each bug are therefore;
For Senn, the equation for the experiment is given as follows ;
5 × t₁ = 92 feet
For Ms. Lady, the equation for the experiment is given as follows;
4 × (t₁ + 4.6) = 92 feet
For Ms. Beetle , the equation for the experiment is given as follows;
4 × (t₁ + 18.4) = 92 feet.
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Answers
Such a ray that divides an angle into two equal angles is called an angle bisector.
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Answer:
undefined
Step-by-step explanation
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Answer:
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Answer:
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Answers
Answer:
Step-by-step explanation:
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Step-by-step explanation:
Find the value of the following:|-15|.
Answers
Answer:
The answer is 15 because that absolute value for anything is 15. No matter what number
Step-by-step explanation:
Li’s family is saving money for their summer vacation. Their vacation savings account currently has a balance of $2,764. The family would like to have at least $5,000.
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Answers
Answer:
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Step-by-step explanation:
Answer:
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Step-by-step explanation:
cause i said so have a problem call my lawyer......
1 is subtracted from a number
Answers
−15 = 5(3q − 10) − 5q
Answers
Answer:
q = 3.5
Step-by-step explanation:
-15 = 5(3q - 10) - 5q
-15 = (5*3q + 5*-10) - 5q
-15 = 15q - 50 - 5q
-15 + 50 = 15q - 5q
35 = 10q
q = 35/10
q = 3.5
Check:
-15 = 5(3*3.5 - 10) - 5*3.5
-15 = 5(10.5 - 10) - 17.5
-15 = 5*0.5 - 17.5
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Answers
Answer:
1 st car is your answer to the question
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Answers
Step-by-step explanation:
C = 25p
p = number of people
C = Total cost of admission
For 4 people, Total cost is
C = 25 × 4 = 100 dollars
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Answers
Answer:
116
Step-by-step explanation:
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Answers
If you do the long division correctly, you will get 105 and all you have is 4 left.
Since you are dividing by 61, you do 4/61.
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I hope this helps!
Vivian's sales territory produced $1.8
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much does she earn if she has a base
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a.)
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Answer:
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Step-by-step explanation:
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to check if its right
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Answers
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Answers
Answer:
11.
A) EZ Pay Plan=0.15x
B) 40 to Go Plan=0.05x+40
12.
0.15x=0.05x+40
13.
x=400 minutes
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Step-by-step explanation:
For 11, what you need to know is that the slope (coefficient of x) is the price per minute. 0.15 per minute and 0.05 per minute are charged, and therefore are the slope for those equations. The 40 on B is because it is the y intercept. No matter how long you use the object, you will always pay at least 40 dollars.
For 12, you have to find x for the minutes used.
For 13, if you do the process algebraically,
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0.10x=40 (subtracted 0.05x from both sides)
x=400 (divided 0.10x and 40 by 0.10)
For 14, (no explanation)
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Answers
Answer:
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Step-by-step explanation:
Answer:
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Step-by-step explanation:
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Step-by-step explanation:
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Answers
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Step-by-step explanation:
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Apply the division operation to get
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Reduce the term of the numerator
⇒ ( 10⁴) / (10⁻⁵)
⇒ ( 10⁴) × (10⁵)
⇒ ( 10⁴⁺⁵)
⇒ 10⁹
Hence, there 8 × 10⁴ would be 10⁹ times as large as 4 × 10⁻⁵ which is determined by the division operation.
To learn more about the division operation click here :
brainly.com/question/25870256
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Answers
Answer:
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Step-by-step explanation:
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Answer:
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<1 and 2
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Answers
Answer:
∠3 and ∠4
Step-by-step explanation:
In this diagram, angles 3 and 4 are the only pair whose sum is 90°.
In this given figure, [tex]\angle{3}[/tex] and [tex]\angle{4}[/tex] are the only pairs of angles that have the measure of 90°.
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Answers
Answer: x=1991/10
Step-by-step explanation: Step 1: Simplify both sides of the equation.
9x+10=2001−x
9x+10=2001+−x
9x+10=−x+2001
Step 2: Add x to both sides.
9x+10+x=−x+2001+x
10x+10=2001
Step 3: Subtract 10 from both sides.
10x+10−10=2001−10
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Step 4: Divide both sides by 10.
10x
10
=
1991
10
x=
1991
10
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Step-by-step explanation:
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Answer:(
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Step-by-step explanation:
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Answers
Answer:
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Step-by-step explanation:
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A fence for a rectangular garden with one side against an existing wall is constructed by using 60 feet of fencing. What is the maximum area that can be enclosed
Answers
Step-by-step explanation:
A fence for a rectangular garden with one side against an existing wall is constructed by using 60 feet of fencing.
Perimeter of rectangle (3 sides)= 60 feet
Let 'x' be the width of the wall
[tex]Perimeter = 2(length)+2(width)\\60=2(length)+2x\\\\60-2x=2(length)\\\frac{60-2x}{2} =length\\Length =30-x[/tex]
Formula for the area of the rectangle is
[tex]Area=length \cdot width\\A=length(x)[/tex]
Replace the length we got using perimeter
[tex]A=(30-x)(x)\\A(x)= 30x-x^2[/tex]
To find out the maximum are we take derivative
[tex]A'(x)= 30-2x\\0=30-2x\\-30=-2x\\x=15[/tex]
find out second derivative to check whether x=15 is maximum
[tex]A''(x)=-2[/tex]
second derivative is negative
So, Maximum area at x=15
To find maximum area we plug in 15 for x in A(x)
[tex]A(x)=30x-x^2\\A(15)=30(15)-15^2\\A(15)=225[/tex]
So, maximum area is 225 square feet