Complete the square to transform the quadratic equation into the form (x – p)2 = q.x2 + 4x - 19 = 5
Answers
Answer:
62
Step-by-step explanation:
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Answers
12.
Explanation:
Let x be the integer she inputs.
"One less than triple the input" would be 3x-1.
She gets 3 as the output; this means 3x-1=3.
To solve this, add 1 to each side:
3x-1+1=3+1
3x=4
Divide both sides by 3:
3x/3 = 4/3
x=4/3 = 1 1/3.
This will not work, however, as it is not an integer.
"One more than half the number" is 1/2x+1. Since she gets 3 as the output, this gives us:
1/2x+1=3
Subtract 1 from each side:
1/2x+1-1=3-1
1/2x=2
Divide both sides by 1/2:
When dividing fractions, flip the second fraction and multiply:
x=2÷(1/2) = 2×(2/1) = (2/1)×(2/1) = 4/1 = 4
While this is an integer, this does not work either, because this expression is for inputs that are even but not divisible by 4. This is divisible by 4, so it is not accurate.
"One-fourth of the input" is 1/4x. The output is 3, which gives us:
1/4x =3
Dividing both sides by 1/4, we have:
When dividing fractions, we flip the second fraction and multiply:
x=3÷(1/4) = 3×(4/1) = (3/1)×(4/1) = 12/1 = 12
This expression is for an input that is divisible by 4. 12 is divisible by 4, so this is accurate.
Final answer:
Given the scenario, no valid integer input would result in an output of $3 from Dorothy's ? button on her calculator. The three conditions specified do not match any integer when the output is $3.
Explanation:
Given that the output of the ? button on Dorothy's calculator is $3, one thing that could have been input and fit one of the conditions is 4, because when an integer is divisible by 4, the calculator outputs its one-fourth. Since 4 is divisible by 4 and one-fourth of 4 equals 1, that's not correct. Now let's check the condition for even numbers not divisible by 4. The calculator outputs 1 more than half the number. So, if we plug in $3 as the output and solve the equation, we get: 3 = 1 + 1/2 (input). Solving for the input, we get 2*2 = 4, which is still wrong. So, finally, we check the condition for odd numbers. Here, the calculator outputs 1 less than triple the input. Substituting $3 as the output, we solve for the input: 3 = 3*(input) - 1. Solving for input, we get input = 4/3, which is not an integer. Therefore, there could not have been an integer input that resulted in a $3 output in this case.
Learn more about Calculator Function here:
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Answer:
Step-by-step explanation:
Step 1: Factor
Answer:
Step-by-step explanation:
x²+18x+80= 0
x²+10x+8x+80=0
x(x+10) +8(x+10)=0
(x+10)(x+8)=0
G. x + y = 25
H. x^2 + y = 25
J. x^2 + y^2 = 5
K. x^2 + y^2 = 25
Answers
That distance is √(3² + 4²) = √(9 + 16) = √25 = 5 .
The equation of a circle centered at the origin is
x² + y² = (radius)²
So this circle is [ x² + y² = 25 ]
That's Choice-'K'.
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Simple Interest Rate: 4.5%
Time: 10 years
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There are a number of ways that you can find out what 4.5% is, you can either divide $2300 by 100, and then multiply by 4.5, or you can find 1%, and multiply by 4.5.
Personally, I think that doing it the first way is easier. $2300/100= 23. 23*4.5= $103.50
Therefore, the interest for 1 year is $103.50.
In order to find what ten years is, you simply have to multiply this by 10. $103.50*10= $1035
To find the total value, you simply have to add the original investment ($2300) and the interest ($1035) together. $2300+$1035= $3335
Therefore, the total of the investment after 10 years is $3335.
Hope this helps :)