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Ierofanga [76]
3 years ago
13

Line k has a slope of 2/3. If line m is parallel to line k, then it has a slope of

Mathematics
2 answers:
Karolina [17]3 years ago
6 0

Answer:  The correct option is (C) \dfrac{2}{3}.

Step-by-step explanation:  Given that line k has a slope of \dfrac{2}{3}. and line m is parallel to line k.

We are to find the slope of line m.

We know that

if two straight lines are parallel, then they have equal slopes.

Since line m is parallel to line k, so we must have

slope of line m = slope of line k.

Therefore, we get

Slope of line m is equal to \dfrac{2}{3}.

Thus, (C) is the correct option.

Kaylis [27]3 years ago
3 0
Line k is // to line m.

Slopes of // lines are equal.

Answer: 2/3
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For the parallelogram ABCD the extensions of the angle bisectors AG and BH intersect at point P. Find the area of the parallelog
natita [175]

Answer:

The area of a parallelogram is 360 in.²

Step-by-step explanation:

Where DG = GH

GP = 12 in.

AB = 39 in.

∠DAB + ∠ABC = 180° (Adjacent angles of a parallelogram)

Whereby ∠DAB is bisected by AG and ∠ABC is bisected by BH

Therefore, ∠GAB + ∠HBA = 90°

Hence, ∠BPA = 90° (Sum of interior angles of a triangle)

cos(\angle GAB) = \dfrac{AP}{AB} = \dfrac{AP}{39} = \dfrac{GP}{GH} =\dfrac{12}{GH}

We note that ∠AGD = ∠GAB (Alternate angles of parallel lines)

∴ ∠AGD = ∠AGD since ∠AGD = ∠GAB (Bisected angle)

Hence AD = DG (Side length of isosceles triangle)

The bisector of ∠ADG is parallel to BH and will bisect AG at point Q

Hence ΔDAQ  ≅ ΔDGQ ≅ ΔGPH and AQ = QG = GP

Hence, AP = 3 × GP = 3 × 12 = 36

cos(\angle GAB) = \dfrac{AP}{AB} = \dfrac{36}{39}

\angle GAB = cos^{-1} \left (\dfrac{36}{39}  \right )

∠GAB = 22.62°

cos(\angle GAB) =  \dfrac{36}{39} = \dfrac{12}{GH}

GH =  \dfrac{39}{36} \times {12}

GH = 13 in.

∴ AD 13 in.

BP = 39 × sin(22.62°) = 15 in.

GH = √(GP² + HP²)

∠DAB = 2 × 22.62° = 45.24°

The height of the parallelogram = AD × sin(∠DAB) =  13 × sin(45.24°)

The height of the parallelogram = 120/13 =  9.23 in.

The area of a parallelogram = Base × Height = (120/13) × 39 = 360 in.²

7 0
3 years ago
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It’s either 64 or 192 if that helps because it say she buys a three week ad would u times 64 by three I’m sorry I don’t have a final answer
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3 years ago
4. solve<br> e) 4^x-10.2^x+16=0<br> I think the dot means multiply?
suter [353]
4^x-10\cdot2^x+16=0\Rightarrow(2^2)^x-10\cdot2^x+16=0\Rightarrow(2^x)^2-10\cdot2^x+16=0

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What is the area of this
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Area is base x height divide by 2
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3 0
2 years ago
HELP ASAP
Natalija [7]

Answer:

The equation of the function: y = mx + b

  • m = slope = (y₂ - y₁)/(x₂ - x₁) = [5 - (-3)]/(4 - 0) = (5 + 3)/4 = 8/4 = 2
  • b = y-intercept = -3

Therefore, the equation is <u>f(x) = 2x - 3</u>

When x = 0, f(x) = 2(0) - 3 = <u>-3</u>

When x increases by 1, f(x) increases by <u>2</u> (slope = the rate of change)

5 0
2 years ago
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