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The sum of four consecutive odd integers is -72 Write an equation to model this situation and find the values of the four integers?
LAzyDaisy123
let n = first odd number; n + 2 = 2nd odd number ,etc.
n + n+2 + n+4 + n +6 = 4n + 12 = -72
4n = -84
n = -21
-21,-19,-17 and -15
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∙ 8y ago
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Any value or values that make an equation or inequality true?
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What are 4 consecutive even integers where the product of the two smaller number is 72 less than the product of the two larger numbers?
12, 10, 8 and 6 (in descending order).Let the highest number equal a.We are told that ab - cd = 72However, as the numbers are consecutive even integers we also know that:b = a - 2c = a - 4d = a - 6thus we can use this to write the above equation in terms of only one variable, a, as:(a * (a - 2)) - ((a-4) * (a-6)) = 72(a2 - 2a) - (a2 - 10a + 24) = 72 (Remember that as we expand the second bracket in the next step we will multiply each term by the minus outside the bracket giving:)a2 - 2a - a2 + 10a - 24 = 72 (Now we can continue to simplify to get:)8a - 24 = 728a = 96a = 12Once we have a value for "a" we have a value for all the variables:a = 12b = 10c = 8d = 6As a proof, if we wish, we can substitute these values back into the original equation to get:ab - cd = 72(12 * 10) - (8 * 6) = 72120 - 48 = 72.
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The square of the third of three consecutive integers is equal to twenty-five more than the product of the first two. What are the integers?
Let the three consecutive integers be a, b, & c. Square of c is 25 more than a*b:c2 = 25 + a*b; also the integers are consecutive, so a+1 = b & b+1 = cput a & b in terms of c, so b = c-1 & a = b-1 = c-2, substitute these into original equation:c2 = 25 + (c-2)*(c-1) = 25 + c2 - 3*c +2 --> c2 = 27 + c2 - 3*c --> 0 = 27 - 3*cc = 9 and from the 'consecutive' equations: b = 8& a = 7Substitute these values back into the original equation to make sure it works.92 = 81 and 8*7 = 56. 81 is 25 more than 56.
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Find 2 consecutive even integers whose sum is 66?
Two identical integers whose sum is 66 are 33 and 33. Add 1 and subtract 1. Now you have 32 and 34. Voilà : two consecutive even integers whose sum is 66.**************************************************************My answer here is the same as the answer above, I'm just going to explain in detail how to actually solve a problem like this. Two consecutive even integers would be like 2 and 4 or 632 and 634. See how the numbers come right after each other, that would be a consecutive integer. Since you wanted consecutive even integers, they are 2 even numbers that come after each other. Now, to solve your problem, the 'formula' for finding 2 consecutive even (and odd, plain consecutive integers would be different) integers for the sum of 66 would be:x + x+2 = 66. First, you add like terms. What I mean, is that you add all your x values and all your normal numbers, which gets us:2x + 2 = 66 Now, you have a normal 2-step equation. To solve a 2-step equation, first you tik-tok. This means if you have any subtraction, you change it so that you add negatives instead(none here). For example 6x-3 changes into 6x + -3. Then you add like terms, which I already explained somewhere above (none here). Then, you add the opposite of your lonesome number(number without a variable) to both sides of the equation. So for example here, you add -2 to both sides of the equation so that you can get rid of that lonesome number, like here:2x + (2 + -2)=66 + -2 -----> 2x = 64 ( no need to put + 0) Now all you have left to do is divide both sides of the equation by the coefficient of the x term, here being 2. LOOK TO SEE IF IT's POSITIVE OR NEGATIVE!!!!:2x = 64-------- X=32 So if your original equation was x + x+2 = 66, you just2 2plug in the numbers in the equation. So:x=32, 32+ 32+2 = 66 -----> 32+34=66 ------> Your 2 consecutive numbers are 32 and 34. Hope I helped. I know it's a looong answer, but I like things to be explained :-)
What would be a real-world situation that could be modeled by the equation 650 10m60m 400?
That's not an equation by definition. It may be a term for something, but alone neither the letters nor values mean anything.
What is an equation that's true for all values?
an equation that's true for all values is an identity.
What does solve the equation mean?
Find values for the variable that satisfy the equation, that is if you replace those values for the variable into the original equation, the equation becomes a true statement.
What is the graph of an equation?
The graph of an equation is a visual representation of the values that satisfy the equation.
What is the meaning of solution of an equation?
The solution to an equation consists of the value (or values) of all the variables such that the equation is true when the variable(s) take those values.
Explain how the values of the slope affect the overall meaning of the equation?
how the values of the slope affect the overall meaning of the equation?
What is the solution to the equation?
It is the set of values for all the variables in the equation which make the equation true.
