Ask question

Ask question

All categories

3 years ago

7

What is one point that lies in the solution set of the

1 answer:

Vlad [161]3 years ago

8 0

Substitute the given point (3, -2) in each condition
(i) y < -3; y ≤ (2/3)x - 4
-2 < -3 → False
Therefore, it is not a solution.
[Since the values of x and y must satisfy both the conditions, if one of them does not satisfy the condition then it is not necessary to check the other one.]
(ii) y > -3; y ≥ 2/3x - 4
-2 > -3 → True
y ≥ 2/3x - 4
-2 ≥ -2 → True
Therefore, it is a solution.
(iii) y < -3; y ≥ 2/3x - 4
-2 < -3 → False
Therefore, it is not a solution.
(iv) y > -2; y ≤ 2/3x - 4
-2 > -2 → False
Therefore, it is not a solution.
Thereofore, the system of linear inequalities having the point (3, -2) in its solution set is y > -3; y ≥ 2/3x - 4. Hope it helps you.

You might be interested in

Which expression is equivalent to (81x4y16)12 for all positive values of x and y?<br> 40.5x4y16

IrinaVladis [17]

Answer:

$(81x^4y^{16})^{\frac{1}{2}} = 9 x^2 y^8$

Step-by-step explanation:

Given

$(81x^4y^{16})^{\frac{1}{2}}$

Required

Determine an equivalent expression

Express 81 as $9^2$

$(9^2x^4y^{16})^{\frac{1}{2}}$

Apply law of indices

$9^2^{\frac{1}{2}} * x^4^{\frac{1}{2}} * y^{16}^{\frac{1}{2}}$

$9^{\frac{2*1}{2}} * x^{\frac{4*1}{2}} * y^{\frac{16*1}{2}}$

$9^{\frac{2}{2}} * x^{\frac{4}{2}} * y^{\frac{16}{2}}$

$9^1 * x^2 * y^8$

$9 * x^2 * y^8$

$9 x^2 y^8$

Hence:

$(81x^4y^{16})^{\frac{1}{2}} = 9 x^2 y^8$

4 0

3 years ago

Simplify the expression shown. You must show your work to receive credit.

ZanzabumX [31]

ANSWER

$12 \sqrt{5}$

EXPLANATION

The given expression is

$\sqrt{2} \times \sqrt{72} \times \sqrt{5}$

The middle radical contains a perfect square.

$\sqrt{2} \times \sqrt{36 \times 2} \times \sqrt{5}$

$\sqrt{2} \times \sqrt{36} \times \sqrt{2} \times \sqrt{5}$

$6\sqrt{2} \times \sqrt{2} \times \sqrt{5}$

Note that:

$\sqrt{a} \times \sqrt{a} = a$

$6\times 2 \sqrt{5} = 12 \sqrt{5}$

4 0

3 years ago

Which expression is equivalent to log_5(x/4)^2?

viktelen [127]

For this case we must find an expression equivalent to:

$log_ {5} (\frac {x} {4}) ^ 2$

So:

We expanded $log_ {5} ((\frac {x} {4}) ^ 2)$ by moving 2 out of the logarithm:

$2log_ {5} (\frac {x} {4})$

By definition of logarithm properties we have to:

The logarithm of a product is equal to the sum of the logarithms of each factor:

$log (xy) = log (x) + log (y)$

The logarithm of a division is equal to the difference of logarithms of the numerator and denominator.

$log (\frac {x} {y}) = log (x) -log (y)$

Then, rewriting the expression:

$2 (log_ {5} (x) -log_ {5} (4))$

We apply distributive property:

$2log_ {5} (x) -2log_ {5} (4)$

Answer:

An equivalent expression is:

$2log_ {5} (x) -2log_ {5} (4)$

3 0

3 years ago

4. Determine the circumference of a circle with a radius that is 14.2 yds. Use 3.14 for π. Round to the nearest tenth.

Vladimir79 [104]

Answer:

The circumference would be around 90 yards.

Step-by-step explanation:

C = 2πr

r = 14.2

14.2 × 3.14 = 44.588

44.588 × 2 = 89.176

89.176 ≈ 90

C = 90

7 0

3 years ago

Equation in slope intercept form of (-3,4) and (1,4)

crimeas [40]

The two points have the same y coordinate, which means that the line is horizontal, which means that the slope is 0.

So, the equation is y=4

4 0

3 years ago

Read 2 more answers