MATHEMATICS HIGH SCHOOL

Distance between (1,2) and (4,6)

Answers

Answer 1

Answer:

Answer:

Step-by-step explanation:

6-4 over 2-1

2 over 1

I hope this is correct and have a great day

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What is the square root property of:

Answers

The square root property seems to be another name for completing the square

x^2 + 5x + 6 = 0

We move the constant to the other side

x^2 + 5x = -6

We square half the linear coefficient and add that to both sides

x^2 + 5x + (5/2)^2 = -6 + 25/4

Now the left side is a perfect square,

(x + 5/2)^2 = 1/4

Here's the square root property part, we take the square root of both sides, remembering the ±

x + 5/2 = ± 1/2

x = -5/2 ± 1/2

Answer: x = -3 or x=-2

We check by plugging in these values to the original equation, and they work.

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x^2 + 6x = 16

Again we add half the linear coefficient, squared, to both sides

x^2 + 6x + 3^2 = 16 + 9

(x + 3)^2 = 25

Here comes the square root property, taking the square root of both sides:

x + 3 = ±5

x = -3 ± 5

x = 2 or x = -8

Again we check by substitution, and they both work

Answer: x = 2 or x = -8

Five times a number is added to two times its square. if the result is 168, find the number

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5x+(2x)^2= 168 now solve this

An airline flies between 6 airports. How many different flight paths can it offer, if it lands three times and never stays in the same place twice?

Answers

Answer:

the airline can offer 20 different flight paths under the given conditions.

Step-by-step explanation:

If the airline has 6 airports and the plane lands three times without staying in the same place twice, this is essentially a permutation problem. You want to find the number of ways to arrange 3 distinct airports out of 6.

This can be calculated using the formula for permutations of "n" items taken "r" at a time:

nPr = n! / (n - r)!

Where "n" is the total number of items (airports in this case) and "r" is the number of items to be arranged (3 landings in this case), and "!" denotes factorial.

So, in your case, the calculation would be:

6P3 = 6! / (6 - 3)!

= (6 * 5 * 4 * 3 * 2 * 1) / (3 * 2 * 1)

= 120 / 6

= 20

So, the airline can offer 20 different flight paths under the given conditions.

Jan bought a blazer for $39.90. The price of the blazer was $38. What sales-tax rate was she charged for this blazer percentage wiese

Answers

Answer:

5% sales-tax rate was she charged for this blazer

Step-by-step explanation:

As per the statement:

Jan bought a blazer for $39.90.

The price of the blazer was $38.

Sales tax price = 39.90 - 38 = $1.90

We have to find the sales-tax rate was she charged for this blazer percentage wise.

Using formula:

$\text{Sales tax rate} = \frac{\text{Sale tax}}{\text{Price of the blazer}} * 100$

Substitute the given value we have;

$\text{Sales tax rate} = (1.90)/(38) * 100 = 5\%$

Therefore, 5% sales-tax rate was she charged for this blazer percentage wise

The question asks for sales tax rate. Sales tax is 39.90-38=1.90 and that's taxed onto the original $38 so 1.9/38=0.05
5% tax on the blazer

Simplify
(1/81) to the 1/4 power

Answers

${ \left( \frac { 1 }{ 81 } \right) }^{ \frac { 1 }{ 4 } }\n \n =\sqrt [ 4 ]{ \frac { 1 }{ 81 } } \n \n =\frac { 1 }{ 3 }$

This is because...

$\frac { 1 }{ 3 } * \frac { 1 }{ 3 } * \frac { 1 }{ 3 } * \frac { 1 }{ 3 } =\frac { 1 }{ 81 }$

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