Part 1:
A. Like terms must have the same variable and exponent.
B. Give an example of two terms that cannot be combined: 7c and 4b
C. Write one complete sentence to explain why the two terms you wrote cannot be combined: 7c and 4b cannot be combined because they have different variables, and are therefore not like terms.
D. Use distributive property: 2(-4 + 6.1) + 3(5 - x)
2 * -4 = -8
2 * 6.1 = 12.2
-8 + 12.2 + 3(5 - x)
3 * 5 = 15
3 * x = 3x
-8 + 12.2 + 15 -3x
-8 + 12.2 = 4.2
4.2 + 15 = 19.2
19.2 - 3x is the simplest version.
Part 2:
A. Thor is wrong because, in step 4, he subtracted to isolate the variable when he should have divided.
B. 4x + 9 = 6
Step 1: 4x + 9 - 9 = 6 - 9
Step 2: 4x = -3
Step 3: 4x/4 = -3/4
Step 4: x = -0.75
10/2=5
5/2=2.5
2.5/2=1.25
1.25/2=.625
.625/2=.3125 meters hope it helps
so it traveled a total of 9.6875.
hope this helps
Answer: 7(11x + 3) .
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Explanation:
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We are asked to: "Factor the expression: 77x + 21 ."
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Upon examination of <u>both</u>: "<u><em>77x</em></u>" and "<u><em>21</em></u>" ; we can see that "<u><em>7</em></u>" is the greatest common factor (GCF) of BOTH. We can examine this visually, but let us write this out:
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21: 1, 3, <em><u>7</u></em>, 21
77x ;
or simply: 77: 1, <u><em>7</em></u>, 11, 77
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So, to proceed:
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Write down a: "7" ;
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7 *( ????)
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Note the distributive property of multiplication:
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a(b+c) = ab + ac ; AND:
a(b - c) = ab - ac ;
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So , we write down a "7" ;
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7*( ???
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The first value is: "+77x" ; so, " 7 * ? = 77x ?" ;
We can examine this visually and realize that the value is "11x";
or we can divide, as follows: (77x/ 7 = 11x ).
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So we have already written down: 7* (??? )
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We can down rewrite as: " 7 * (11x ......)
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(since " 7 * 11x = 77x ") ;
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The next (and in our case, final !) value in our expression is:
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" +21 " ;
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We have written down: 7* (11x ......)
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So now, we need to determine: "7 * ? = 21" ?
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We can inspect visually and determine the value is: "3" ;
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Or we can solve by division, as follows:
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"7 * ? = 21 ?" ; 21 / 7 = ? ; 21 / 7 = 3 . The value is: "3" .
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So , we have: " 7 * (11x .....) " ; now we can rewrite as:
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" 7*(11x + 3)" ; or, simply: " 7(11x +3)" ; The multiplication is implied).
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The answer is: 7(11x +3) .
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Does our answer make sense? Let us check!
The answer; " 7(11x +3) " is the factored expression of: "(77x + 21)" ;
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So: " 7(11x +3) " should EQUAL "77x +21 " . Is this true??
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Remember the distributive property of multiplication:
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a(b+c) = ab +ac ;
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So; " 7(11x +3) " = (7*11x) + (7*3) ; which equals:
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77x + 21 . Yes!
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Answer:
4 seconds.
Step-by-step explanation:
The function f(x)=-10(x)(x-4) ........ (1), represents the approximate height of a projectile launch on the ground into the air as a function of time in seconds x.
Now, we are asked that for how long from the launch does the projectile stays in the air.
Therefore, we have to solve the equation (1) making f(x) as zero.
Hence, 10x(x - 4) = 0
⇒ x = 0 or x = 4
(As x can not be zero since at x = 0 sec, the projectile was at the ground.}
Hence, x = 4 seconds.
Therefore, the projectile was in the air for 4 seconds. (Answer)