Which statement is true about the regular octagon?

Select the point that is a solution to the system of inequalities

Zarrin [17]

<h2>Hello!</h2>

The answer is:

The point that is a solution to the system of inequalities is C(4,2).

To find the point that is a solution to the system of inequalities, we need to evaluate it into the given inequalities. If the point is a solution to the system of inequalities, both inequalities will be satisfied.

We are given the inequalities:

$y\leq 2x-2$

$y\leq x^{2} -3x$

So, substituting the given points into the given inequalities, we have:

- A. (2,1)

Substituting into the first inequality, we have:

$y\leq 2x-2\\\\1\leq 2*(2)-2\\\\1\leq 4-2\\\\1\leq 2$

Substituting into the second inequality, we have:

$y\leq x^{2} -3x$

$1\leq (2)^{2} -3(2)$

$1\leq 4 -6$

$1\leq -2$

Therefore, since 1 is not less or equal to -2, the point A(2,1) is not a solution to the system of inequalities.

- B. (-2,-1)

Substituting into the first inequality, we have:

$y\leq 2x-2\\\\-1\leq (-2)*(2)-2\\\\-1\leq -4-2\\\\-1\leq -6$

Substituting into the second inequality, we have:

$y\leq x^{2} -3x$

$-1\leq (-2)^{2} -3(-2)$

$-1\leq 4 +6$

$-1\leq 10$

Therefore, since -1 is not less or equal to -6, the point B(-2,-1) is not a solution to the system of inequalities.

- C. (4,2)

Substituting into the first inequality, we have:

$y\leq 2x-2\\\\2\leq (4)*(2)-2\\\\2\leq 8-2\\\\2\leq 6$

Substituting into the second inequality, we have:

$y\leq x^{2} -3x$

$2\leq (4)^{2} -3(4)$

$2\leq 16 -12$

$2\leq 4$

Therefore, since 2 is less than 6, and 2 is less than 4, the point B(4,2) is a solution to the system of inequalities.

- D(1,3)

Substituting into the first inequality, we have:

$y\leq 2x-2\\\\3\leq (1)*(2)-2\\\\3\leq 2-2\\\\3\leq 0$

Substituting into the second inequality, we have:

$y\leq x^{2} -3x$

$3\leq (1)^{2} -3(1)$

$3\leq 1 -3$

$3\leq -2$

Therefore, since 3 is not less than 0, and 3 is not less than -2, the point D(1.3) is not a solution to the system of inequalities.

Hence, the point that is a solution to the system of inequalities is C(4,2).

Have a nice day!

6 0

3 years ago

Alice has x dolar in her accout she spend $35.31 to buy medicines for her gradmothe rif the balance in her account is $161.23, w

PolarNik [594]

Answer:

Alex had $196.54 in her account before the purchase.

Step-by-step explanation:

Given:

Amount spend on medicines = $35.31

Balance Amount Remaining = $161.23

We need to find the amount in her account before purchase.

Solution:

Let the amount in her account before purchase be 'x'.

Now we can say that;

Amount in her account before purchase minus Amount spend on medicines is equal to Balance amount remaining.

framing in equation form we get;

$x-35.31=161.23$

Now by Using Addition property of equality we will add both side by 35.31 we get;

$x-35.31+35.31=161.23+35.31\\\\x=\$196.54$

Hence Alex had $196.54 in her account before the purchase.

6 0

3 years ago

Solve the equation for x.<br>5x - ( 4x - 1) = 2 help please

ValentinkaMS [17]

Answer:

x = 1

Step-by-step explanation:

Given

5x - (4x - 1) = 2 ← distribute the parenthesis by - 1

5x - 4x + 1 = 2

x + 1 = 2 ( subtract 1 from both sides )

x = 1

4 0

4 years ago

What’s is 2 1/2 divided 1/3

Marat540 [252]

Answer:

7 $\frac{1}{2}$

Step-by-step explanation:

$2\frac{1}{2} *$ the reciprocal of $\frac{1}{3}$

To find reciprocal, flip the top and the bottom.

So $\frac{1}{3}$ would be $\frac{3}{1}$ .

Multiply like normal.

6 0

4 years ago

Write the absolute value function as a piecewise function f(x)=7|x|

Evgesh-ka [11]

Answer:

10x<9x>=-3

Step-by-step explanation:

6x +4x <-3 (5x-8>=-3

10x<-3(-3x>=-3

multiple the bracket by -3

10x<9x>-3

7 0

3 years ago