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ludmilkaskok [199]
3 years ago
6

Andy is solving a quadratic equation using completing the square. If a step in the process results in 169/9 = (x – 6)2, could th

e original quadratic equation be solved by factoring? Explain your reasoning.
Mathematics
2 answers:
natta225 [31]3 years ago
8 0
Yes the equation can be solved by factoring. Using the given equation take the square root of both sides. Both 169 and 9 are perfect squares so the left side becomes plus or minus 13/3 which is rational. Six plus 13/3 is also a rational number. If the solutions of a quadratic equation are rational then the equation is factorable. Please mark a good rating and brainlest
svp [43]3 years ago
3 0

Both169 and 9 are perfect squares.

The square root of 169/9 is rational.

Six plus 13/3 is a rational number, and 6 minus 13/3 is also a rational number.  

If the solutions of a quadratic equation are rational, then the equation is factorable.

You might be interested in
Two angles are supplementary. One is 56° more than three times three times the other. Find the measures of the angles.
kaheart [24]
Supplementary means they equal 180 when added. Therefore:

X+56+3x=180
Combine common units
4x+56=180
Subtract 56 from both sides
4x=124
Divide by 4
X=31

Now we know the smaller angle is 31 degrees. Now we plug that into the larger angle:
3(31)+56
93+56
149

The larger angle is 149 degrees.

I hope this Helps!
8 0
3 years ago
Nicholas used a $10 bill to pay for a granola bar that only costs p dollars. How much change did Nicholas receive from the cashi
BARSIC [14]
10 - p.
Nicholas would have spent $p, so he has $p less than $10!
3 0
3 years ago
Read 2 more answers
Keisha, Scott, and Ryan have a total of $101 in their wallets. Keisha has $6 more than Scott. Ryan has 3 times what Scott has. H
Yuri [45]

Answer:

Keisha =$25

Scott =$19

Ryan = $57

Step-by-step explanation:

Let the amount each have be represented by A, B and C

Keisha = A

Scott = B

Ryan = C

Keisha , Scott and Ryan have a total of $101.

That’s

A + B + C = $101

Keisha has $6 more than Scott

A = 6 + B

Ryan has 3 times Scott

C = 3B

Substitute 6+B for A and 3B for C in the first equation.

That’s

A + B + C = 101

6 + B + B + 3B = 101

6 + 5B = 101

Subtract 6 from both sides

6 - 6 + 5B = 101 - 6

5B = 95

Divide both sides by 5

B = 95/5

B = 19

Scott has $19

Recall Keisha has $6 more than Scott B.

That’s A = 6 + B

A = $6 + $19

A = $25

Keisha has $25

Also, Ryan C has 3 times what Scott B has .

That’s

C = 3 x B

C = 3 x 19

C = $57

Therefore, Keisha has $25, Scott has $19 and Ryan has $57

3 0
3 years ago
Find the perimeter of the polygon
wariber [46]

Answer:

56 yds

Step-by-step explanation:

Simply add up all the sides to find your perimeter:

12 + 12 + 18 + 14 = 56

8 0
4 years ago
PLEASEEEEE HELP ASAP!!! IM NOT GOOD AT MATH AND I DONT UNDERSTAND THIS PROBLEM!!!! PLEASE HELP!!!!!
Elan Coil [88]
You need to use the law of sines.
First, we find the measures of the angles x.
x + x + 100 = 180
2x + 100 = 180
2x = 80
x = 40

Now we set up an equation based on the law of sines.

\dfrac{a}{\sin A} = \dfrac{b}{\sin B} = \dfrac{c}{\sin C}

We know one angle (100 deg) and its opposite side (750,000 miles).
Then we know another angle (40 deg) and need to find the opposite side (d).

\dfrac{d}{\sin 40^\circ} = \dfrac{750,000}{\sin 100^\circ}

Now we solve for d. Multiply both sides by sin 40.

d = \dfrac{\sin 40^\circ}{\sin 100^\circ} \times 750,000

Answer: The first choice.
5 0
3 years ago
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