Answer:
When six guests choose cheesecake and eight choose apple pie, the ratio is 6:8. If we use the same prompt but change 6 to 3 and change 8 to 4, the ratio becomes 3:4 with the pie graph looking exactly the same.
6:8 comes out to a total of 14 people
and 3:4 comes out to a total of 7 people
The two ratios are equivalent due to the graphs looking exactly the same as well as that 14 is double of 7.
Step-by-step explanation:
Domain is X
Range is Y
Therefore {-3,-1,1}
Remember you don’t repeat numbers if there is more than one
Additive inverse means the sum should be 0
so all you gotta do is multiply the complex number by -1
(the question isn't clear so I can't state the option)
Answer: The number is: 4 ¼ ; or, write as 4.25 .
<span>_____________________________________________
</span>Explanation:
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We set up the problem as:
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5(x − 2) = 7+ x ; Solve for "x" (our "unknown number"; which is the answer).
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Using the "distributive property of multiplication" :
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a*(b + c) = ab + ac ; AND:
a* (b − c) = ab − ac ;
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Let us take the "left-hand side" of our equation and expand it:
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5(x − 2) = (5*x) − (5*2) = 5x − 10 ;
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and rewrite the equation; substitute our "expanded value" for the "left-hand side";
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→ 5(x − 2) = 7+ x ; ↔ 5x − 10 = 7+ x ;
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Now, subtract "x" from EACH SIDE of the equation; & add "10" to EACH SIDE of the equation;
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→ 5x − 10 − x + 10 = 7+ x − x + 10 ;
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→ to get: 4x = 17 ;
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→ Now, divide EACH side of the equation by "4"; to isolate "x" on one side of the equation; and to solve for "x" (our answer);
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→ 4x / 4 = 17 / 4;
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→ x = 17/4 = 17 ÷ 4 = 4 ¼ ; or, write as 4.25 .
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→ Answer: The number is: 4 ¼ ; or, write as 4.25 .
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→Let us check our answer:
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"Five times the difference of a number and 2" ;
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→ 5* (x − 2) = 5 * (4.25 − 2) = 5 * (2.25) = 11.25 ;
→ Is "11.25" , SEVEN MORE THAN 4.25??
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→ 11.25 − 4.25 =?? 7 ??? Yes!
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Answer:
Step-by-step explanation:
We don't need choices to find out the correct answer. Solve this problem by completing the square. Begin by setting the quadratic equal to 0 and moving over the constant, like this:
and factor out the -1 in front of the x-squared, since the leading coefficient HAS to be a 1:
Now take half the linear term, square it, and add it to both sides. Our linear term is -2. Half of -2 is -1, and squaring that gives us 1. So we add a 1 into both sides. But that -1 out front there on the left is a multiplier, so what we actually added in was -1(1) which is -1:
On the left side we have a perfect square binomial, which is why we do this, and on the right side we have -2:
and we can move that constant back over and set the quadratic back equal to y:
which gives us a max height of 2.
(If this was modeling parabolic motion, we would know that the time it takes to get to that max height is 1 second. The vertex of this parabola is (1, 2))
