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Angelina_Jolie [31]
3 years ago
6

Please use the photo and do the prove for #13 because I’m having a really hard time. Thanks!

Mathematics
1 answer:
rewona [7]3 years ago
7 0

∠2 = ∠3 | Given

∠1 + ∠2 = 180 | Supplementary Angles Postule (If two angles are adjacent and                  ∠3 + ∠4 = 180|                                                        linear, they're supplementary)

∠1 + ∠2 = ∠3 + ∠4 | Transitive property

∠1 + ∠3 = ∠3 + ∠4 | Substitution property

∠1 = ∠4 | Subtraction Property

∠2 = ∠3 | Supplementary Congruent Theorem

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A rectangular tract of land in Mathville has the dimensions 4x2 + 3x + 12 and 4x – 2. Another rectangular area of a land in Alge
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Answer:

Step-by-step explanation:

Area of a rectangle = Length * Width

Given the dimension

Length = 4x2 + 3x + 12

Width = 4x – 2

A) Area =  (4x^2 + 3x + 12)(4x – 2)

Open the parenthesis

= 16x^3-8x^2+12x^2-6x+48x-24

Area of land in Mathville = 16x^3+4x^2+42x-24

For the land in Algebratown

Area =  (5x^2 + x – 4)(2x + 1)

Area = 10x^3+5x^2+2x^2+x-8x-4

Area  = 10x^3+7x^2-7x-4

B) difference between the area of Mathville and the area of Algebratown

= 16x^3+4x^2+42x-24 -(10x^3+7x^2-7x-4)

= 16x^3+4x^2+42x-24 -10x^3-7x^2+7x+4

collect like terms

= 16x^3-10x^3+4x^2-7x^2+42x+7x-24+4

= 6x^3-3x^2+49x-20

C) The difference if x = 9

Substitute x = 9 into the resulting function

A(x) = 6x^3-3x^2+49x-20

A(9) = 6(9)^3-3(9)^2+49(9)-20

A(9) = 2187-243+441-20

A(9) = 2,365

Hence the difference of the areas if x = 9 is 2,365

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3 years ago
Which ordered pair is a solution of the equation y = 4x - 3?
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Answer:

(0,-3)

(1,1)

(2,5)

Step-by-step explanation:

They're all correct. it doesn't matter which one you choose.

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3 years ago
4. A six-meter-long ladder leans against a building. If the ladder makes an angle of 60° with the
serious [3.7K]
Rather than memorize sines and cosines of various common triangles, I prefer to remember the simple derivation of those formulas…

Imagine that the wall is a mirror, so you have one ladder leaning against the wall and you also have the reflection of that ladder leaning behind it. Now the ladder is 6m long, its reflection is 6m long, and if the distance between their bases is also 6m then you have a 60–60–60 equilateral triangle. And, good news, the problem says that the base angle is 60 degrees. So the real part in front of the mirror is half of the equilateral triangle, which means the distance from the base to the mirror is 3m. And then the height is sqrt(36–9) = sqrt(27) = 3*sqrt(3).

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You are watering a garden. The height h (in feet) of water spraying from the garden hose can be modeled by h(x)=−0.1x2+0.7x+3, w
swat32

Answer:

g(x) = -0.1x^2 + 0.5x + 3.6

Step-by-step explanation:

Given

h(x) = -0.1x^2 + 0.7x  + 3

Required

Determine the new function

From the question, we understand that the new function wants the water to hit the ground 1 ft farther.

1 ft farther implies x + 1

So, in the given function, we substitute x + 1 for x in h(x) = -0.1x^2 + 0.7x  + 3

This gives:

h(x + 1) = -0.1(x + 1)^2 + 0.7(x + 1)  + 3

Expand Bracket

h(x + 1) = -0.1(x + 1)(x + 1) + 0.7(x + 1)  + 3

h(x + 1) = -0.1(x^2+2x+1) + 0.7(x + 1)  + 3

h(x + 1) = -0.1x^2-0.2x-0.1 + 0.7x + 0.7  + 3

Collect Like Terms

h(x + 1) = -0.1x^2-0.2x + 0.7x + 0.7  + 3-0.1

h(x + 1) = -0.1x^2 + 0.5x + 3.6

Hence, the new function is:

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