To solve these problems, we must remember the distributive property. This property states that a coefficient being multiplied by a polynomial in parentheses is equal to the sum of the coefficient times each of the separate terms. Using this knowledge, let's begin with number 21:
-(4x + 17) + 3(7-x)
To begin, we should distribute the negative sign through the first set of parentheses and the coefficient of positive 3 through the second set of parentheses.
-4x - 17 + 21 - 3x
Next, we must combine like terms, or add/subtract the constants terms and the variable terms in order to create a more concise expression.
-7x + 4 (your answer)
Now, we can move on to question 22 and solve it in a similar manner:
7(2n-8) - 4(12 - 8n)
Again, we will distribute the coefficients through the parentheses. However, keep in mind that the coefficient in front of the second set of parentheses is actually a NEGATIVE 4, so we must distribute the negative as well.
14n - 56 - 48 + 32n
Next, we will combine like terms (add the n terms together and subtract the constant terms).
46n - 104
Now, we can solve problem 23:
8 + 2(5f - 3)
We will again distribute through the parentheses:
8 + 10f - 6
Combine like terms after that:
10f + 2
Therefore, your answers for the three problems are as follows:
21) -7x + 4
22) 46n - 104
23) 10f + 2
Hope this helps!
<em>Congruent triangles</em> are two or more triangles with the same length of <u>sides</u> and measure of internal <u>angles</u>. Thus the <em>required</em> proof is as shown below:
From the given diagram, it can be <u>observed</u> that:
AB = AC (<em>similar</em> property of two lines)
AC = AE (<u>similar </u>property of two lines)
Also,
m<A is a <u>common</u> angle to ΔABC and ΔADE
So that it can be <em>concluded </em>that;
ΔABC ≅ ΔADE (Side-Angle-Side property)
Thus since ΔABC ≅ ΔADE are <u>congruent</u>, then;
BC = DE (<u>corresponding</u> sides of <em>congruent</em> triangles)
For further clarifications on congruent triangles, visit: brainly.com/question/1619927
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Answer:
$60
Step-by-step explanation:
set up a proportion and cross-multiply:
3000/400 = cost/450
c = cost
3,000c = 180,000
c = 180/3
c = 60
Answer:
12. 5x
13. 5/x-z
Step-by-step explanation:
12. product means multiplication so multiply 5 by x= 5x
13. quotient means division and difference means subtraction. so you divide 5 by x-z= 5/x-z
