Answer:
960 peopleStep-by-step explanation:
If each side of the basketball arena is 20 ft. X 30 ft, the area of each side of the basketball arena = 20ft * 30ft = 600ft².
Since all the four sides are filled with people, the total area of the 4 sides will be expressed as 4*600 = 2400ft²
If each person takes up 2.5ft², total number of people in the arena will be gotten by simply dividing the area of all the four sides by the area took up by each person.
Total number of people in the arena = area of all the four sides by the area/ area took up by each person.
Total number of people in the arena = 2400/2.5
Total number of people in the arena = 960 people.
Hence there are approximately 960 people in the arena.
PLEASE ANSWER QUICK Part A: If (62)x = 1, what is the value of x? Explain your answer. (5 points) Part B: If (60)x = 1, what are the possible values of x? Explain your answer. (5 points)
Answer:
The first one is 0, the second one is ARN (All real numbers)
Step-by-step explanation:
1. Anything raised to the "zeroth" power is always 1
2. Because 7 is being raised to the zeroth power, the number inside the parentheses becomes 1. Now x can equal anything, 1 times itself will always equal 1, no matter how many times you multiply them.
Equations can have one, zero or infinitely many solutions.
a: The value of x is 0b: x has infinitely many solutions[tex](a)\ (6^2)^x = 1[/tex]
Express 1 as [tex]6^0[/tex]
[tex](6^2)^x = 6^0[/tex]
Express 0 as 2 x 0
[tex](6^2)^x = 6^{2 \times 0}[/tex]
Open the bracket
[tex]6^{2 \times x} = 6^{2 \times 0}[/tex]
Cancel out 6 on both sides
[tex]2 \times x =2 \times 0[/tex]
Divide both sides by 2
[tex]x =0[/tex]
Hence, the value of x is 0
[tex](b)\ (6^0)^x = 1[/tex]
Express [tex]6^0[/tex] as 1
[tex]1^x = 1[/tex]
Express [tex]1^x[/tex] as 1
[tex]1 = 1[/tex]
Both sides of the equation are the same
This means that:
x has infinitely many solutions
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what is 7 x 4 pleez i nid help
Answer:
28
Step-by-step explanation:
if you do 7 + 7 + 7 + 7 that equals 28.
Jesip bought 3 boxes of cereal for $2.49 each, 1.5
pounds of meat for $4.56, 5 apples for $0.67 each,
and 5 yogurts for $6. How much did he spend at the
store?
Answer:
45.57
Step-by-step explanation:
3 x 2.49 =7.47
4.65
5 x 0.67 = 3.35
5 x 6 = 30
7.47+ 4.65 + 3.35 + 30 = 45.47
When positive integer A, which has n digits, is multiplied by (n+2) , the product is a number with (n+1) digits, all of whose digits are (n+1) . How many instances of A exist?
Answer:
A = 95238 (only)
Step-by-step explanation:
The question is equivalent to asking what n-digit number consisting only of the digit n will be divisible by n+1. Of the numbers 1, 22, 333, 4444, ... 999999999, the only one is 666666, which is divisible by 7.
The 5-digit integer A is 666666/7 = 95,238. There is only one instance of A.
A company offered 200 cameras at a 15% discount during a 5-day sale
The bar graph shows the number of cameras sold at the end of each day.
Day 1 - 30
Day 2 - 40
Day 3 - 50
Day 4 - 25
Day 5 - 40
(a) Find the percentage increase in the number of cameras sold on Day 5 as compared to Day 4.
Answer:
60%
Step-by-step explanation:
Cameras sold on Day 4 = 25, on Day 5 = 40
The difference in numbers of sold cameras = 40 - 25 = 15
The increase is 15 cameras.
Percentage increase:
15/25*100% = 60%Answer is 60% increase on Day 5 compared to Day 4
Simplify the radical expression.
Answer:
9√3
Step-by-step explanation:
√(81*3)
√81*√3
9√3
Suppose the following facts to be true: $\bullet$ The probability of a random kindergartener having chicken pox at any given time is $2\%$. $\bullet$ Among kindergarteners who have chicken pox, $75\%$ have red spots. $\bullet$ Among kindergarteners who do not have chicken pox, $1\%$ have red spots. Given that Sanjay, a kindergartener, has red spots, what is the probability that Sanjay has chicken pox? Enter your answer as a fraction in simplified form.
Question
Suppose the following facts to be true: The probability of a random kindergartener having chicken pox at any given time is 2%. Among kindergarteners who have chicken pox, 75% have red spots. Among kindergarteners who do not have chicken pox, 1% have red spots. Given that Sanjay, a kindergartener, has red spots, what is the probability that Sanjay has chicken pox? Enter your answer as a fraction in simplified form.
Answer:
75/124
Step-by-step explanation:
This is a question based on conditional Probability
We would solve this using Bayes's Theorem of Conditional Probability
From the above question, we have the following information:
The probability of a random kindergartener having chicken pox at any given time is 2%.
Hence, the probability that a kindergartner would not have chicken pox
= 100% - 2%
= 98%
Kindergarteners who have chicken pox, 75% have red spots.
Kindergarteners who do not have chicken pox, 1% have red spots.
The Sanjay, a kindergartener, has red spots, the probability that Sanjay has chicken pox is calculated as:
= (Probability of a random kindergartener having chicken pox at any given time ⋂ Probability of kindergarteners who have chicken pox, and have red spots)/ [(Probability of a random kindergartener having chicken pox at any given time ⋂ Probability of kindergarteners who have chicken pox, and have red spots) + (Probability Kindergarteners who do not have chicken pox and have red spots ⋂ Probability that a kindergartner would not have chicken pox)
= (2% × 75%)/[(2% × 75%) +( 1% × 98%)]
= 150/150 + 98
= 150/248
= 75/124
(8x-5y)(3x+7y) Polynoimal Equation Distribution
Step-by-step explanation:
i guess that is the correct answer
On a zip-line course, you are harnessed to a cable that travels through the treetops. You start at platform A and zip to each of the other platforms. How far do you travel from Platform B to Platform C? (Including your steps would be helpful)
Answer:
The distance from Platform B to Platform C is 26.926 units
Step-by-step explanation:
The given parameters are;
The zip-line course distance from platform A to platform F are given;
On the given graph of the path of travel we have;
Coordinates of the point B = (-25, -20) and the coordinates of the point C = (-15, 5)
The distance between two points with coordinates (x₁, y₁) and (x₂, y₂) is given by the formula;
[tex]l = \sqrt{\left (y_{2}-y_{1} \right )^{2}+\left (x_{2}-x_{1} \right )^{2}}[/tex]
Therefore, the distance between B and C is found by substituting (-25, -20) = (x₁, y₁) and (-15, 5) = (x₂, y₂)
Which gives;
[tex]l = \sqrt{\left (5-(-20) \right )^{2}+\left ((-15)-(-25) \right )^{2}} = 26.926 \ units[/tex]
The distance from points B to C = 26.926 units.
L and M are complementary, L = 2x + 25, and M = 4x + 11. Determine the measure of each angle.
L =
M=
HELP
Answer:
[tex]L = 43[/tex] and [tex]M = 47[/tex]
Step-by-step explanation:
Given
[tex]L = 2x + 25[/tex]
[tex]M = 4x + 11[/tex]
Required
Determine the values of L and M
Since L and M are complementary, we have that
[tex]L + M = 90[/tex]
Substitute values for L and M
[tex]2x + 25 + 4x + 11 = 90[/tex]
Collect Like Terms
[tex]2x + 4x = 90 - 11 - 25[/tex]
[tex]6x = 54[/tex]
Divide both sides by 6
[tex]x = \frac{54}{6}[/tex]
[tex]x = 9[/tex]
Substitute 9 for x in the expressions of L and M
[tex]L = 2x + 25[/tex]
[tex]L = 2 * 9 + 25[/tex]
[tex]L = 18 + 25[/tex]
[tex]L = 43[/tex]
[tex]M = 4x + 11[/tex]
[tex]M = 4 * 9 + 11[/tex]
[tex]M = 36 + 11[/tex]
[tex]M = 47[/tex]
Use the position equation given below, where s represents the height of the object (in feet), v0 represents the initial velocity of the object (in feet per second), s0 represents the initial height of the object (in feet), and t represents the time (in seconds), as the model for the problem. s = −16t2 + v0t + s0 An aircraft flying at 900 feet over level terrain drops a supply package.
(a) How long does it take until the supply package to strike the ground? (Round your answer to three decimal places.) t = sec
(b) The aircraft is flying at 158 miles per hour. How far does the supply package travel horizontally during its descent? (Round your answer to one decimal place.) ft
Answer:
(a) 7.5 seconds
(b) The horizontal distance the package travel during its descent is 1737.8 ft
Step-by-step explanation:
(a) The given function for the height of the object is s = -16·t² + v₀·t + s₀
The initial height of the object s₀ = 900 feet
The initial vertical velocity of the object v₀[tex]_y[/tex] = 0 m/s
The time it takes the package to strike the ground is found as follows;
0 = -16·t² + 0×t + 900
900 = 16·t²
t² = 900/16 = 62.25
t = √62.25 = 7.5 seconds
(b) Given that the horizontal velocity of the package is given as 158 miles/hour, we have
158 miles/hour = 231.7126 ft/s
The horizontal distance the package covers in the 7.5 second of vertical flight = 231.7126 ft/s × 7.5 s = 1737.8445 feet = 1737.8 ft to one decimal place
The horizontal distance the package travel during its descent = 1737.8 ft.
I don't understand by when it's saying the cost of the amount of lemonade cups and advertising
Set G is the set of positive integers divisible by 4 and Set F is the set of perfect
squares. List the first 5 elements of set H, which contains numbers in G that are
also elements of F.
Greetings from Brasil...
G = {4; 8; 12; 16; 20; 24; 28; 32; 36; 40; 44; 48; 52; 56; 60; 64; 68; 72; 76; 80; 84; 88; 92; 96; 100; 104; ...}
F = {1; 4; 9; 16; 25; 36; 49; 64; 81; 100; ...}
So, according to the statement, it is desired:
G ∩ F - the intersection between the 2 sets, that is, which numbers are present simultaneously in the 2 sets....
Looking at the sets we conclude that
G ∩ F = {4; 16; 36; 64; 100}OBS: note that in truth G are the multiples of 4
Graph Z=3cos315+3isin315 explain where you would find this equation on a complex plane
Answer:
cos 315° = 45° reference angle in the 4th quadrant = √2 /2
And sin 315° is the negative of this
So
z = (3) cos 315° + ( 3i ) sin 315° =
[ (3/2)√2 , - (3/2) √2 i ]
In the problem 12 - 16, what number is negative? *
Answer:
[tex]-16[/tex]
Step-by-step explanation:
[tex]12-16[/tex]
We can first look at the number that is higher.
[tex]16[/tex]
16 is negative because it is the number that is higher and is being subtracted from 12.
So your answer is
[tex]-16[/tex]
• Kiana goes to the library. She borrows 5 books about planets
and 2 books about dinosaurs. How many books does Kiana
borrow in all?
• What is the unknown in this problem?
number of books about planets
number of books about dinosaurs
number of books in all
Answer:
1. The total is the unknown which is 7
5 books about planet
2 books about dinosaurs
7 number of books in all
Number of books about planets is 5, Number of books about dinosaurs is 2, and Number of books in all is 7.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given that Kiana goes to the library.
The number of books Kiana borrow about planets is 5 books.
The number of books Kiana borrow about dinosaurs is 2 books.
we need to find the number of books bought in all.
We need to add the books.
5 books + 2 books
7 books.
Number of books about planets is 5.
Number of books about dinosaurs is 2.
Number of books in all is 7.
Hence, Number of books about planets is 5, Number of books about dinosaurs is 2, and Number of books in all is 7.
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Let ABCD be a parallelogram such that AB = 10,BC = 14, and \angle A = 45. Find the area of the parallelogram. please write your answer as a root. NOT a decimal.
Answer:
[tex]70\sqrt{2}[/tex]
Step-by-step explanation:
Since angle A is 45, the height of the base BC is 10/[tex]\sqrt{2}[/tex] by 1-1-sqrt(2) triangles.
Then we can apply parallelogram area formula.
=====================================================
Explanation:
One formula you can use is
A = b*c*sin(theta)
where angle theta is between sides b and c
Note how angle A is between sides AB = 10 and AD = BC = 14.
------------
Using that formula gives
A = b*c*sin(theta)
A = 10*14*sin(45)
A = 140*sin(45)
A = 140*sqrt(2)/2 ... use unit circle
A = (140/2)*sqrt(2)
A = 70*sqrt(2)
solve 1/3x - 1 = 3/5
[tex]\frac{1}{3}x-1=\frac{3}{5}\\ \\5x-15=9\\\\5x=9+15\\\\5x=24\\\\x=\frac{24}{5}\\ \\x=4\frac{4}{5}[/tex]
a shopkeeper bought a purse for rupees 240 and sold it for rupees 220 find his loss or profit in percent
Answer:
8 1/3 %
Step-by-step explanation:
Since he bought for 240 and sold for 220, decrease is 20 Rupees.
20/240 = 1/12
100/12 = 8.33333 (Repeated)
0.33333 (repeated) = 1/3
8 1/3 %
Hope this helps!
Use Pythagorean Theorem to find the length of the missing side of this right triangle to the nearest tenth.
Answer:
10.3
Step-by-step explanation:
Pythagorean Theorem:
[tex]a^{2} + b^{2} = c^{2} \\[/tex]
a and b being the sides and c being the hypotenuse.
[tex]3.9^{2} + b^{2} = 11^{2}[/tex]
15.21 + [tex]b^{2}[/tex] = 121
[tex]b^{2}[/tex] = 121 - 15.21
[tex]b^{2}[/tex] = 105.79
b = [tex]\sqrt{105.79}[/tex]
b = 10.3
Hope that helped!!! k
Factorise -75ab² - 15ac
5a(3b - c)
-15b²(3a + c)
-15a(5b² + c)
15a(5b² - c)
A triangle has a base of length 6 cm and an area of less than 12 cm². Which of the following gives the height h of the triangle
h < 4 cm
h < 6cm
h < 12 cm
h < 24 cm
Expand (2x-3)(2x +3)
4x² + 12x + 9
4x² - 12x – 9
4x² - 9
4x² + 9
A woman buys 8 tubers of yam at #200 each and sells them at a profit of 12%. Calculate the selling price.
#192
#1600
#1792
#2000
What is the size of each angle of a regular 15-sided polygon?
78⁰
156⁰
185⁰
200⁰
The height of a boy is t cm. His father is two times his height. Express the height of the father in terms of t.
5t cm
2t cm
t cm
t² cm
Factorise 4am² - 6am
2am(2m – 3)
m²(2a - 3m)
am²(4 - 6a)
2a²m²(2m - 3)
What is the slant height of a cone of height 8cm and base diameter of 12cm?
5 cm
6 cm
8 cm
10 cm
Express 51 x 10⁻⁵ as a decimal number.
0•000051
0•00051
0•0051
0•51
A television costs #54 000. A 12¹/₂% discount is given for cash. What is the cash price ?
# 54 000
# 47 000
# 47 250
# 6 750
Find y-intercept in the graph below

(0, 1)
(0, 5)
(5, 0)
(0, 2)
Simplify - 40pq ÷ (-2)²
-10p
-10q
-10pq
10pq
Express the product of 0•003 and 0•045 in standard form.
3•45 x 10⁵
1•35 x 10⁵
1•35 x 10⁻⁵
1•35 x 10⁻⁴
Submission Tracking ID - DO NOT CHANGE *
This is important for tracking purposes. Do not change. Any change in this will make your submission void
Which of these is the three figure bearing of the acute-angle bearing N40⁰W ?
320⁰
310⁰
270⁰
040⁰
The volume of a cylinder is 700π cm³. What is the base diameter of the cylinder if its height is 7 cm ?
6•5 cm
7cm
10 cm
20 cm
What is the LCM of 2x²y, 3xy² and 4x²y ?
16x²y²
12x²y²
12x²y
7xy
Express 636 000 in standard form.
6.36 x 10⁻⁵
6.36 x 10⁻⁴
6.36 x 10⁴
6.36 x 10⁵
A cone and a cylinder have equal volumes and radii. The height of the cone is 12 cm. What is the height of the cylinder?
4 cm
12 cm
36 cm
50 cm
Find the angle measured clockwise between the directions: N and SW
45°
135°
180°
225°
What is the total surface area of a cylinder opened at one end if its height is 20cm and it's diameter is 14cm (π = 3¹/₇)
880 cm²
1034 cm²
1188 cm²
1250 cm²
I think of a number. I then double it. The result is 58. What number did I think of ?
29
20
16
10
RSTU is a quadrilateral as seen below. What is the value of X?

5
10
11
15
Answer:
1) -15·a·(5·b² + c)
2) h < 4
3) 4·x² - 9
4) 1792
5) 156°
6) 2t cm
7) 2·a·m·(2·m - 3)
8) 10 cm
9) 0.00051
10) #47,250
11) -10·p·q
12) 1.35 × 10⁻⁴
13) 320°
14) 20 cm
15) 12·x²·y²
16) 6.36 × 10⁵
17) 4 cm
18) 225°
19) 1034 cm²
20) 29
Step-by-step explanation:
1) The given expression is -75·a·b - 15·a·c
Which can be expressed as -15·a·(5·b² + c)
2) The height, h < 2 × 12/6 = 4
h < 4
3) (2·x - 3)·(2·x + 3) = 4·x² - 9
4) The selling price = 1.12 × 200 × 8 = 1792
5) The interior angle of a polygon is given by the relation;
(n - 2)×180/n for 15, we get;
(15 - 2)×180/15 = 156°
6) 2t cm
7) 4·a·m² - 6·a·m = 2·a·m·(2·m - 3)
8) Slant height = √(8² + 6²) = 10 cm
9) 51 × 10⁻⁵ = 0.00051
10) Cash price = #54,000 × (1 - 0.125) = #47,250
11) -40·p·q÷(-2)² = -10·p·q
12) 0.003 × 0.045 = 1.35 × 10⁻⁴
13) N40°W = 320°
14) The base diameter of the cylinder = √(4 × (700×π cm³/7)/π) = 20 cm
15) The LCM of 2·x²·y, 3·x·y² is 12·x²·y²
16) 636,000 = 6.36 × 10⁵
17) 1/3·π·r²·h₁ = π·r²·h₂
h₂/h₁ = 1/3·π·r²/( π·r²) = 1/3
h₂/12 = 1/3
h₂ = 12/3 = 4 cm, the height of the cylinder = 4 cm
18) The angle = 180 + 45 = 225°
19) The total surface area = 22/7×14²/4 + 22/7 ×14 × 20 = 1034 cm²
20) The number is 58/2 = 29.
Answer:
9) 51 × 10⁻⁵ = 0.00051
10) Cash price = #54,000 × (1 - 0.125) = #47,250
11) -40·p·q÷(-2)² = -10·p·q
12) 0.003 × 0.045 = 1.35 × 10⁻⁴
13) N40°W = 320°
14) The base diameter of the cylinder = √(4 × (700×π cm³/7)/π) = 20 cm
15) The LCM of 2·x²·y, 3·x·y² is 12·x²·y²
16) 636,000 = 6.36 × 10⁵
17) 1/3·π·r²·h₁ = π·r²·h₂
h₂/h₁ = 1/3·π·r²/( π·r²) = 1/3
h₂/12 = 1/3
h₂ = 12/3 = 4 cm, the height of the cylinder = 4 cm
18) The angle = 180 + 45 = 225°
19) The total surface area = 22/7×14²/4 + 22/7 ×14 × 20 = 1034 cm²
20) The number is 58/2 = 29.
Step-by-step explanation:
19
8
+
5
8
I need help on this fraction equation plz
Answer: [tex]3[/tex]
Add
[tex]19/8+5/8=24/8[/tex]
Divide
[tex]24/8=3[/tex]
Answer:
3
Step-by-step explanation:
To add these fractions, find the LCD (least common denominator). Then divide by 8. You get 3.
So your answer will be 3. Hope this helps!
Find the approximate side length of a square game board with an area of 179in ^2.
Area of a square game board = 179 inches ²
To be calculated:-Calculate the side of given square game board.
Formula applied:-Area of square = ( Side )²
Solution:-We know that,
Area of square = ( Side )²
★ Substituting the value in the above formula, we get :
=> 179 = ( Side )²
=> Side = √179
=> Side = 13.37 inches ( approx )
Answer:
13.38 in
Step-by-step explanation:
The area of a square can be found using the following formula.
[tex]a=s^2[/tex]
where a is the area and s is the side length.
We know that the area of the square is 179 in^2. We can substitute that value in for a.
[tex]179 in^2=s^2[/tex]
We want to find the side length. Therefore, we have to isolate the variable, s.
s is being squared. The inverse of a square is the square root. Take the square root of both sides of the equation.
[tex]\sqrt{179 in^2}=\sqrt{s^2}[/tex]
[tex]\sqrt{179 in^2}=s[/tex]
[tex]13.3790882 in =s[/tex]
We want to find the approximate side length. Round to the nearest hundredth. The 9 in the thousandth place tells us to round the 7 to a 8,
[tex]13.38 in= s[/tex]
The side length of the board game is about 13.38 inches.
An expression is shown.
(2x-3) + [4x(3x+2)]
Which expression is equivalent to the given Expression?
A. 9x-1
B. 14x+5
C. 12x^2 + 2x-1
D. 12x^2 + 10x-3
Answer:
D
Step-by-step explanation:
(2x - 3) + [ 4x(3x + 2)]
2x - 3 + [ (4x*3x) + (4x*2) ]
2x - 3 + [ 12x² + 8x ]
2x - 3 + 12x² + 8x
12x² + 10x - 3
Solve the following system of equations by the addition method.
-3x + 4y = -2
6x - y = 11
What is the value of the x-coordinate?
11/2
-2
2
0
Answer:
x=2
Step-by-step explanation:
help me please I am stuck
Answer is b) 2/5
good luck
how many triangles will be in the 5th set of triangles?
Answer:
25.
Step-by-step explanation:
I am assuming you only mean the small triangles, not the composite ones.
The second triangle set has 3 triangles on bottom row and 1 on the top - total 4.
The 3rd triangle set has 5 triangles on the bottom , 3 on the next up and 1 on the top - total 9
Following the pattern 4th set will have the number of triaNGLES
7 + 5 + 3 + 1 = 16.
So the 5th will have 9 + 7 + 5 + 3 +1 = 25 triangles.
The F-ratio increases as _________. the variability between means increases relative to the variability within groups the variability between means decreases relative to the variability within groups the total variability increases the total variability decreases
Answer: variability between means increases relative to the variability within groups
Step-by-step explanation:
The formula to calculate F-ratio : variance between groups divided by variance within groups
Here, F-ratio [tex]\propto[/tex] is proportional to variance between groups but inversely proportional to variance within groups .
So, F-ratio increases when variability between means increases relative to the variability within groups.
2(х + 4) - 5 = 3х + 3
What’s the answer
Answer:
x = 0
Step-by-step explanation:
Hello!
2(x + 4) - 5 = 3x + 3
Distribute the 2
2x + 8 - 5 = 3x + 3
Combine like terms
2x + 3 = 3x + 3
Subtract both sides by 2x
3 = x + 3
Subtract both sides by 3
0 = x
The answer is x = 0
Hope this helps!
Answer: [tex]x=0[/tex]
Simplify both sides of the equation
[tex]2(x-4)-5=3x+3\\(2)(x)+(2)(4)+-5=3x+3(Distribute)\\2x+8+-5=3x+3[/tex]
[tex](2x)+(8+-5)=3x+3[/tex](Combine Like Terms)
[tex]2x+3=3x+3[/tex]
Subtract 3x from both sides
[tex]2x+3-3x=3x+3-3x\\-x+3=3[/tex]
Subtract 3 from both sides
[tex]-x+3-3=3-3\\-x=0[/tex]
Divide both sides by -1
[tex]-x/1=0/-1\\x=0[/tex]
12. Dreams of driving. Suppose you drive to school. If you
drive at an average speed of 45 mph, you arrive 1 min early
for the first bell. If you drive at an average speed 40 mph,
you arrive 1 min late. How many miles do you live from
school?
Answer: 12 miles
Step-by-step explanation:
Ok, we know that:
Distance = Time*Speed.
or:
D = T*S
The distance between the house and the school is constant, and suppose that T is the exact time such that you arrive just in time, then:
" If you drive at an average speed of 45 mph, you arrive 1 min early for the first bell. "
We can write this as:
D = (T - 1min)*45mi/h.
"If you drive at an average speed 40 mph, you arrive 1 min late."
We can write this as:
D = (T + 1min)*40mi/h.
So we have a system of linear equations:
D = (T - 1min)*45mi/h.
D = (T + 1min)*40mi/h.
First, 1 hour has 60 mins, then 1 min = (1/60) hours.
We do this change because in the system of equations we have minutes and hours, and we can only work with one unit, now we can write the equations as:
D = (T - (1/60)h)*45mi/h.
D = (T + (1/60)h)*40mi/h.
now, we can write:
D = (T - (1/60)h)*45mi/h. = (T + (1/60)h)*40mi/h.
Now we can solve this for T.
(T - (1/60)h). = (T + (1/60)h)*(40/45)
T = (T + (1/60)h)*(40/45) + (1/60)h
T - T*40/45 = (1/60)h*(1 + 40/45) = 0.031 h
T*(1 - 40/45) = 0.031 h
T = 0.031h/(1 - 40/45) = 0.283... hours
Now, to find the distance to the school we can replace this time in one of the equations:
D = (T + (1/60)h)*40mi/h. = (0.283...h + (1/60)h)*40mi/h = 12 miles.