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3 years ago

Which statements are true

Mathematics

2 answers:

nasty-shy [4]3 years ago

5 0

Answer: 1. False.

2.True.

3.True.

4.False.

5.True.

6.False.

Explanation:

1.∠XFG is lying between the one side and the line extended to the next side of the triangle, therefore it is an exterior angle.

2.∠EFG is lying between the two sides of the ΔEFG, therefore it is an interior angle of the triangle.

3.∠FEZ is lying between the one side and the line extended to the other side of ΔEFG.

4.∠YGE is a straight line it is between the one side and the line extended to the same side ∴ it cannot be an exterior angle of the triangle.

5.∠EGF and FGY lying on the same line YZ ,∴they are linear pair i.e. they are supplementary angles.

6.∠FEG and ∠FGE are both the interior angles of a triangle and we know that for supplementary angles they should lie on the same line.Therefore ∠FEG and ∠FGE are not supplementary angles.

algol [13]3 years ago

4 0

1) ∠XFG is an interior angle of ΔEFG. - False

(∠XFG is an exterior angle of ΔEFG since that angle is out of the triangle)

2) ∠EFG is an interior angle of ΔEFG. - True

(∠EFG is an interior angle since it is included in the ΔEFG)

3) ∠FEZ is an exterior angle of ΔEFG. - True

(∠FEZ is an exterior angle as it it is out of the triangle EFG)

4) ∠YGE is an exterior angle of ΔEFG. - False

(∠YGE is not an exterior nor an interior angle since it is a straight line)

5) ∠EGF and ∠FGY are supplementary angles. - False

(∠EGF and ∠FGY do not add up to 180° so they are not supplementary)

6) ∠FEG and ∠FGE are supplementary angles. - False

(∠FEG and ∠FGE do not add up to 180° so they are not supplementary)

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A=1/2 (2x + 4) (6x + 4) solve using FOIL

boyakko [2]

A = 1/2 (12x² + 8x + 24x + 16)
A = 1/2 (12x² + 32x + 16)
A = 6x² + 16x + 8

-----------------------------------------------------------
Answer: 6x² + 16x + 8
-----------------------------------------------------------

7 0

3 years ago

Let S be the solid beneath z = 12xy^2 and above z = 0, over the rectangle [0, 1] × [0, 1]. Find the value of m > 1 so that th

jonny [76]

Answer:

The answer is $\sqrt{\frac{6}{5}}$

Step-by-step explanation:

To calculate the volumen of the solid we solve the next double integral:

$\int\limits^1_0\int\limits^1_0 {12xy^{2} } \, dxdy$

Solving:

$\int\limits^1_0 {12x} \, dx \int\limits^1_0 {y^{2} } \, dy$

$[6x^{2} ]{{1} \atop {0}} \right. * [\frac{y^{3}}{3}]{{1} \atop {0}} \right.$

Replacing the limits:

$6*\frac{1}{3} =2$

The plane y=mx divides this volume in two equal parts. So volume of one part is 1.

Since m > 1, hence mx ≤ y ≤ 1, 0 ≤ x ≤ $\frac{1}{m}$

Solving the double integral with these new limits we have:

$\int\limits^\frac{1}{m} _0\int\limits^{1}_{mx} {12xy^{2} } \, dxdy$

This part is a little bit tricky so let's solve the integral first for dy:

$\int\limits^\frac{1}{m}_0 [{12x \frac{y^{3}}{3}}]{{1} \atop {mx}} \right.\, dx =\int\limits^\frac{1}{m}_0 [{4x y^{3 }]{{1} \atop {mx}} \right.\, dx$

Replacing the limits:

$\int\limits^\frac{1}{m}_0 {4x(1-(mx)^{3} )\, dx =\int\limits^\frac{1}{m}_0 {4x-4x(m^{3} x^{3} )\, dx =\int\limits^\frac{1}{m}_0 ({4x-4m^{3} x^{4}) \, dx$

Solving now for dx:

$[{\frac{4x^{2}}{2} -\frac{4m^{3} x^{5}}{5} ]{{\frac{1}{m} } \atop {0}} \right. = [{2x^{2} -\frac{4m^{3} x^{5}}{5} ]{{\frac{1}{m} } \atop {0}} \right.$

Replacing the limits:

$\frac{2}{m^{2} }-\frac{4m^{3}\frac{1}{m^{5}}}{5} =\frac{2}{m^{2} }-\frac{4\frac{1}{m^{2}}}{5} \\ \frac{2}{m^{2} }-\frac{4}{5m^{2} }=\frac{10m^{2}-4m^{2} }{5m^{4}} \\ \frac{6m^{2} }{5m^{4}} =\frac{6}{5m^{2}}$

As I mentioned before, this volume is equal to 1, hence:

$\frac{6}{5m^{2}}=1\\m^{2} =\frac{6}{5} \\m=\sqrt{\frac{6}{5} }$

3 0

3 years ago

I'll pick brainiest. Please help me!! Answer as best as you can. THANK YOU!!

rodikova [14]

The volume of the cube is 54.87 but rounded to the nearest tenth is 54.9

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3 years ago

Which units should she use to report the distance from the earth to the moon?

Anvisha [2.4K]

Well,

The distance from the earth to the moon, FYI, is over 200,000 miles. That is a LONG distance. We are trying to find a reasonable unit of measurement.

What do we mean by "reasonable?" We mean that that unit should be able to express the distance as a number that is not huge or tiny. In other words, we want it to be as close as possible to 1.

mm, or millimeters, is a tiny unit. It is not reasonable.

cm, or centimeters, is also a tiny unit. It also is not reasonable.

m, or meters, is also a relatively small unit. It also is not reasonable.

km, or kilometers, is the largest of the four. In km, the distance from the earth to the moon is about 363,000 km. That's not too bad.

However, if these weren't the only options, I would choose Mm, or megameters, which would put the distance at 363 Mm.

The correct option is D.

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3 years ago

If your scale factor is negative, the image will be rotated 180 degrees?

Tamiku [17]

Answer:

yes it's rotated 180 degree angle

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3 years ago