Answer: The number is 75
Lets start by defining the 2-digit number.
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Define the number
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Let x be the digit in the tens place and y be the digit in the ones place.
The number is 10x + y
The reverse of the number is 10y + x
Now we will construct the equations needed
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Construct equations
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When the digits are reversed, the value decreases by 18:
(10x + y) - (10y + x) = 18 . ← Apply distributive property
10x + y - 10y - x = 18 ←Combine like terms
9x - 9y = 18 ←Divide by 9 through
x - y = 2
The sum of the digits is 12:
x + y = 12
Now that we have the two equations, we can solve for x and y.
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Solve for x and y
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x - y = 2 ---------------------- (equation 1)
x + y = 12 ---------------------- (equation 2)
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Make x the subject in equation 1
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x - y = 2 ← Add y from both sides
+ y +y
x = 2 + y
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Substitute x = 2 + y into equation 2
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x + y = 12 ← Substitute x = 2 + y
2 + y + y = 12 ← combine like terms
2 + 2y = 12 ← Subtract 2 from both sides
-2 -2
2y = 10 ← Divide by 2 on both sides
÷2 ÷2
y = 5
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Substitute y = 5 into equation 1
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x - y = 2 ← substitute y = 5
x - 5 = 2 ← add 5 on both sides
+5 +5
x = 7
Now we know the value of x and y. Lets find the 2-digit number.
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Find the 2-digit number
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The number = 10x + y = 10(7) + 5 = 75
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Answer: The number is 75
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Answer:
25. 9(2.50) + 9(4) = 58.5. The total cost of the folders and notebooks is $58.50.
26. 5(11.75 + 5) = 83.75. The total cost of the tickets and lunches is $83.75.
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<h2>
Horizontal distance when projectile strikes water surface is 170 .02 feet</h2>
Step-by-step explanation:
The height is given by
We need to find when it strikes the water surface,
At water surface h = 0 feet
Substituting
Solving this quadratic equation to get x.
-32x² + 2500x + 500000 = 0
32x² - 2500x - 500000 = 0
x = 170 .02 feet or x = -91.90 feet
Negative x is not possible
Horizontal distance when projectile strikes water surface = 170 .02 feet
Answer:
A. (x - 3)(x + 3)
Step-by-step explanation:
From the graph the x-axis is crossed by the graph at different points which are;
x = 3 and x = -3
This means the solutions are : x = 3 and x =-3
The factors will form the following equation : (x - 3)(x + 3)
See attached
