Answer:
See below.
Step-by-step explanation:
The graph of the quadratic equation is a parabola or u shaped graph. It has a vertex at (-1,-3) since h=-1 and k=-3 in the vertex form. It is also facing down since the leading coefficient is negative.
Answer:
<u>29</u> $1 bills and <u>14</u> $5 bills.
Step-by-step explanation:
Let 
be the number of $1 bills and 
be the number of $5 bills. With the information given, we can set up two equations:
1) 
2) 
There are two ways to solve it; with elimination or substitution. In this explanation, I will solve it with elimination.
To solve it with elimination, multiply the first equation by 5 to get:
Then, you can subtract the equation we just got by the second equation to get:
Thus, 
. To find y, just substitute x for 29 in the first equation to get:
. Therefore, 
. That means that there are 29 $1 bills and 14 $5 bills. You can check by substituting those values for x and y in either of the first two equations.
Hope this helps :)
70. 180-120=60, and 180-60+50=70
Assuming you are referring to the area of a "trapezoid"; in which one calculates the Area, "A", as follows:
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<span> A = 1/2* h(b1+b2) ;
in which: A = Area = 16 (given);
h = height = 4 (given);
b1 = length of one of the two bases = 3 (given);
b2 = length of the other of the two bases = ? (what we want to solve for) ;
______________________________________________________
Using the formula: </span>A = 1/2 h(b1+b2) ;
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Let us plug in our known values:
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→ 16 = (1/2) * 4*(3 + b2) ; → Solve for "b2".
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→Note: On the "right-hand side" on this equation: "(1/2)*(4) = 2 ."
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So, we can rewrite the equation as:
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→ 16 = 2*(3 + b2) ; → Solve for "b2".
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We can divide EACH side of the equation by "2"; to cancel the "2" on the "right-hand side" of the equation:
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→ 16 / 2 = [2*(3 + b2)] / 2 ; → to get:
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8 = (3 + b2) ;
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→ Rewrite as: 8 = 3 + b2;
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Subtract "3" from EACH side of the equation; to isolate "b2" on one side of the equation; and to solve for "b2" :
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→ 8 - 3 = 3 + b2 - 3 ; → to get:
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b2 = 5; From the 2 (TWO) answer choices given, this value,
"b2 = 5", corresponds with the following answer choice:
____________________
b2= [16-6]/2= 5 ; as this is the only answer choice that has: "b2 = 5".
<span>_________________________________________
As far getting "</span>b2 = 5" from: "b2= [16-6]/2= 5"; (as mentioned in the answer choice), we need simply to approach the problem in a slightly different manner. Let us do so, as follows:
<span>_____________________________________
Start from: </span>A = 1/2 h(b1+b2); and substitute our known (given) values):<span>
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</span>→ 16 = (1/2) *4 (3 + b2) ; → Solve for "b2".
_____________________________
Note that: (½)*4 = 2; so we can substitute "2" for: "(1/2) *4" ;
and rewrite the equation as follows:
_________________________
→ 16 = 2 (3 + b2) ;
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Note: The distributive property of multiplication:
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a*(b+c) = ab + ac ;
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As such: 2*(3 + b2) = (2*3 + 2*b2) = (6 + 2b2).
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So we can substitute: "(6 + 2b2)" in lieu of "[2*(3 + b2)]"; and can rewrite the equation:
______________________
→ <span>16 = 6 + 2(b2) ; Now, we can subtract "6" from EACH side of the equation; to attempt to isolate "b2" on one side of the equation:</span>
<span>________________________________________________
</span>→ 16 - 6 = 6 + 2(b2) - 6 ;
→ Since "6-6 = 0"; the "6 - 6" on the "right-hand side" of the equation cancel.
→ We now have: 16 - 6 = 2*b2 ;
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Now divide EACH SIDE of the equation by "2"; to isolate "b2" on one side of the equation; and to solve for "b2":
____________________
→ (16 - 6) / 2 = (2*b2) / 2 ;
→ (16 - 6) / 2 = b2 ;
→ (10) / 2 = b2 = 5.
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NOTE: The other answer choice given:
_____________
"<span>16= 1/2* 4(3+b2)= 6+2b2" is incorrect; since it does not solve for "b2".</span>
