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3 years ago

6

Which of these ordered pairs is a solution to the linear inequality 3y - 2x > 8?

1 answer:

Tanzania [10]3 years ago

3 0

For this case we have the following inequality:
3y - 2x> 8
The first thing we should do is to graph the function.
Then, see the set of points that are the solution of the inequality.
The solution set is given by the shaded region.
See attached image.
Answer:
Shaded region.
See attached image.

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The angle between a diagonal and the longer base of the isosceles trapezoid MNFD is 45°. NK is an altitude to the longer base. I

Elanso [62]

Answer:

$NK \approx 7.001$ , $MK = 2$ , $MF \approx 7.001$ , $A_{AMNFD} = 49.007$

Step-by-step explanation:

According to the statement, we find the following inputs:

$\angle MDK = \angle DMF = 45^{\circ}$ (Due to the condition of isosceles trapezoid)

$MD = 9$

$NF = 5$

Given than longer base and shorter base are parallel to each other, we conclude that:

$\angle KND = 180^{\circ} -\angle NKD - \angle KDN$

$\angle KND = 180^{\circ}-90^{\circ}-45^{\circ}$

$\angle KND = 45^{\circ}$

$\angle FND = 90^{\circ}-\angle KND$

$\angle FND = 45^{\circ}$ (By definition of complementary angles)

$\angle FND = \angle NFM = 45^{\circ}$ (Due to the condition of isosceles trapezoid)

$\angle MDK = \angle DMF = \angle FND = \angle NFM = 45^{\circ}$

$\angle NOF = \angle MOD = \angle MOF = \angle FOD = 90^{\circ}$ (By definitions of complementary and vertical angles and the theorem that states that sum of internal angles within a triangle equals 180º)

$MO = DO = \frac{\sqrt{2}}{2}\cdot MD$ (By theorem for 45-45-90 Right Triangle)

$NO = OF = \frac{\sqrt{2}}{2}\cdot NF$ (By theorem for 45-45-90 Right Triangle)

If we know that $MD = 9$ and $NF = 5$ , then we find that:

$DO = MO \approx 6.364$

$NO = OF \approx 3.536$

The value of MK is obtained from the following relationship:

$MK = \frac{MD-NF}{2}$

$MK = \frac{9-5}{2}$

$MK = 2$

And the value of KD is calculated from this expression:

$KD = MD-MK$

$KD = 9-2$

$KD = 7$

Now by the Pythagorean Theorem we find that:

$NK = \sqrt{(NO+DO)^{2}-KD^{2}}$

$NK = \sqrt{9.9^{2}-7^{2}}$

$NK \approx 7.001$

And considering the symmetry characteristics of an isosceles trapezoid, we determine MF:

$MF = NO + DO \approx 7.001$

Lastly, the area of the isosceles trapezoid is determined by the following formula:

$A_{AMNFD} = NF\cdot NK + MK\cdot NK$

$A_{AMNFD} = NK\cdot (NF+MK)$

If we know that $NK \approx 7.001$ , $NF = 5$ and $MK = 2$ , then the area of the figure is:

$A_{AMNFD} = (7.001)\cdot (5+2)$

$A_{AMNFD} = 49.007$

8 0

2 years ago

A notebook that costs $0.75 to make in the factory is sold for $1.35.

kvasek [131]

Answer:

a) price markup $0.60

b) percent marked up 180%

Step-by-step explanation:

Amount marked up:

1.35 - 0.75 = $0.60

Percent markup:

0.75x = 1.35

x = 1.8 or 180%

5 0

3 years ago

Correct answer gets Brainliest + 15 points! , help me if u can pls.

xxTIMURxx [149]

Point form: (4,5)
Equation form: x=4, y=5

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2 years ago

Find the slope of the line using the table. (keep as a fraction) CORRECT ANSWER GETS BRAINLIST HURRY BEFORE PEOPLE TAKE IT!!!

rusak2 [61]

Step-by-step explanation:

We notice that when x increases by 3, y decreases by 2.

Hence the slope of the line

= Rise of y / Run of x

= (-2) / (3)

= -2/3.

8 0

3 years ago

HELP HAVING A BAD DAY<br> Write as a monomial in standard form:<br> (–x^2y^3m)^5

natita [175]

Answer: -x^10y^15m^5

4 0

2 years ago

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