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3 years ago

Two lines, R and M, are represented by the following equations:

1 answer:

6 0

Well, i'm just going to take a stab at this:

The answer out of:
> It is (18,9) ,
> It is (9, 18)
I believe both are correct as those are both plausible coordinates (although I may be wrong)

Line R: 2x + 2y = 18 (x + y = 9)
Line M: x + y = 9
There are infinite many solutions as they are the same line.

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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

3 years ago

Will mark brainliest for whoever answers

nata0808 [166]

bBBBBBBStep-by-step explanation:

4 0

3 years ago

In Triangle XYZ, m triangles?<br> O XYZ = TUV<br> O XYZ = VUT<br> O No congruency statement can be made because only two angles

ahrayia [7]

Answer:

No congruency statement can be made because the side lengths are unknown.

Step-by-step explanation:

We are given the measure of two angles in ∆XYZ, as 90 and 30 respectively. The 3rd angle can be known without being given. Since sum of angles in a triangle is 180°, the 3rd angle would be 180 - (90+30) = 60°.

Same applies to ∆TUV.

We only know the 3 angles of each triangle, but we are not given any of the side lengths. Therefore, we cannot make any congruency statement since the side lengths are unknown.

6 0

3 years ago

Math geometry placemats

madam [21]

Let's call the missing side ? as shown in the problem.

Now set up a equation where everything adds up to 28x+11

?+8x+2+8x+2+5x+12=28x+11

?+21x+16=28x+11

?=28x-21x+11-16

?=7x-5

So 7x-5 is the missing side!

Hope it helps :D

5 0

3 years ago

If the regular price is 4.19 and the mark down is 35% what is the sale price

vaieri [72.5K]

1.46 would be taken away so the marked down price would be 2.73

7 0

3 years ago