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liq [111]
3 years ago
12

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

inal quadratic equation be solved by factoring? Explain your reasoning.
Mathematics
2 answers:
Zarrin [17]3 years ago
7 0
<span>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 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. </span>
UkoKoshka [18]3 years ago
4 0

Answer:

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.

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Mr. Chen filled a wading pool with 20 gallons of water. How many pints of water did he put in a pool
eduard

Answer:

160 pints

Step-by-step explanation:

Every 1 gallon = 8 pints.

20x8=160

8 0
3 years ago
Read 2 more answers
If f(x)3(=- Vx-3, complete the following statement:x + 2f(19) ==Answer here
Digiron [165]
Explanation

This exercise is about evaluating a function at a particular argument. To do that, we replace the variable with the argument in the formula of the function, and simplify.

Let's do that:

\begin{gathered} f(19)=\frac{3}{19+2}-\sqrt[]{19-3}, \\  \\ f(19)=\frac{3}{21}-\sqrt[]{16}, \\  \\ f(19)=\frac{1}{7}-4, \\  \\ f(19)=\frac{1-28}{7}, \\  \\ f(19)=-\frac{27}{7}\text{.} \end{gathered}Answerf(19)=-\frac{27}{7}\text{.}

8 0
1 year ago
The table shows the different types of shoes available at a family shoe store.
Wittaler [7]

Answer:

about 48.6%

Step-by-step explanation:

20 women's shoes are athletic.

35 women's shoes are formal.

52 women's shoes are casual.

The total number of women's shoes is 107.  So the probability that a randomly selected one is casual is:

P = 52/107

P ≈ 48.6%

6 0
3 years ago
Joni earns $300 per week. If she gets a 25% raise, how much more money will she earn each week?
alina1380 [7]

Answer:

\huge\boxed{$75}$75

Step-by-step explanation:

Joni currently earns $300 per week (given)

To find how much more she will earn each week, write an expression adding the original pay and the raise amount.

$300 + 25%

Find 25 as a decimal for multiplication

25%  = 25/100 = 0.25

Write an expression to represent the scenario

Expression example 1:

$300 + 0.25(300)

This expression adds the original pay and the new raise together.

Expression example 2:

$300 (1.25)

This expression already takes the new pay into account by finding 125% of the original pay.

Simplify both expressions

Expression 1:

$300 + 0.25(300)

$300 + $75

$375

Expression 2:

$300 (1.25)

$375

Both expressions represent the same scenario and therefore come out to the same result. Now that we know how much Joni made after the raise, we need to find how much more money she will earn in a week with the following equation.

New amount - original amount = amount increase

Substitute known values into the equation

$375 - $300

Simplify

$75

Joni will earn $75 more each week.

Let me know if you have any questions!

3 0
3 years ago
Read 2 more answers
if the perimeter of the rectangle was known to be 90 in what would the value of x be in order for this to be true​
Fofino [41]

Answer:

x = 30 in

Step-by-step explanation:

length of rectangle is (2/3)x + 10; width is (1/3)x + 5;

perimeter is 90 in; find x:

P = 90 in = 2(2/3)x + 2(10) + 2(1/3)x + 2(5), or

      90 in = (6/3)x + 30 in

Solving for x, we get (2)x = 60 in, or x = 30 in

8 0
3 years ago
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