Find the equation of the line through point (-4,-4) and perpendicular to 2x+3y=3

In △ABC, AB = 13.2m,

luda_lava [24]

Answer:

(i) ∠ABH = 14.5°

(ii) The length of AH = 4.6 m

Step-by-step explanation:

To solve the problem, we will follow the steps below;

(i)Finding ∠ABH

first lets find <HBC

<BHC + <HBC + <BCH = 180° (Sum of interior angle in a polygon)

46° + <HBC + 90 = 180°

<HBC+ 136° = 180°

subtract 136 from both-side of the equation

<HBC+ 136° - 136° = 180° -136°

<HBC = 44°

lets find <ABC

To do that, we need to first find <BAC

Using the sine rule

$\frac{sin A}{a}$ = $\frac{sin C}{c}$

A = ?

a=6.9

C=90

c=13.2

$\frac{sin A}{6.9}$ = $\frac{sin 90}{13.2}$

sin A = 6.9 sin 90 /13.2

sinA = 0.522727

A = sin⁻¹ ( 0.522727)

A ≈ 31.5 °

<BAC = 31.5°

<BAC + <ABC + <BCA = 180° (sum of interior angle of a triangle)

31.5° +<ABC + 90° = 180°

<ABC + 121.5° = 180°

subtract 121.5° from both-side of the equation

<ABC + 121.5° - 121.5° = 180° - 121.5°

<ABC = 58.5°

<ABH = <ABC - <HBC

=58.5° - 44°

=14.5°

∠ABH = 14.5°

(ii) Finding the length of AH

To find length AH, we need to first find ∠AHB

<AHB + <BHC = 180° ( angle on a straight line)

<AHB + 46° = 180°

subtract 46° from both-side of the equation

<AHB + 46°- 46° = 180° - 46°

<AHB = 134°

Using sine rule,

$\frac{sin 134}{13.2}$ = $\frac{sin 14.5}{AH}$

AH = 13.2 sin 14.5 / sin 134

AH≈4.6 m

length AH = 4.6 m

8 0

2 years ago

What is the area of a parallelogram if is length is x+1 and height is x+8?

Irina-Kira [14]

Answer:

8 square units

Step-by-step explanation:

x + 1 = 0

x = -1

x + 8 = 0

x = -8

Area = (-1) * (-8) = 8 square units

3 0

2 years ago

On an algebra test , the highest grade was 50 points higher than the lowest the sum of the two grades was 122 find the lowest gr

KATRIN_1 [288]

Answer:

Highest grade: 86

Lowest grade: 36

Step-by-step explanation:

Let the highest grade be h, lowest grade be l.

$h = 50 + l \\ \\ h + l = 122 \\ h = 122 - l \\ \\$

Therefore,

$122 - l \: = 50 + l \\ 2l \: = 72 \\ l = 36 \\ \\ h = 36 + 50 = 86$

6 0

2 years ago

Explain the Error: Jayme tells her friend that ordered pairs that have an x-coordinate of O lie on the x-axis. She uses the orig

Paul [167]

Answer:

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Step-by-step explanation:

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4 0

2 years ago

Which of the following represents the zeros of the function

umka21 [38]

<span>g(x) = x^3 - 9x^2 + 2x + 48 ?

Probe some roots. When you use x = - 2

you will have: (-2)^3 - 9(-2)^2 + 2(-2) + 48 = -8 - 36 - 4 + 48 = 0

So, - 2 is a root

From that you can divide x^3 - 9x^2 + 2x + 48 by x + 2 and you will get

x^2 - 11x + 24

Then you can factor that: (x - 8)(x - 3)

So, the three roots are x = - 2, x = 3 and x = 8, which is the option B.

Answer: option B. x = 8, x = -2 , and x = 3
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3 0

3 years ago