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3 years ago

The slope of a line that is parallel to each line whose equation is given

Mathematics

1 answer:

Kobotan [32]3 years ago

3 0

Parallel lines, slope is the same so
1) 3x+8y = 12
8y = -3x + 12
y = -3/8(x) + 3/2, slope = -3/8

slope of a line that is parallel = -3/8

2)5x+4y = 5
4y = -5x + 5
y = -5/4(x) + 5/4; slope is -5/4

slope of a line that is parallel = -5/4
--------------------
perpendicular, slope is opposite and reciprocal

3)
3x+8y = 11
8y = -3x + 11
y = -3/8(x) + 11/8. slope = -3/8
slope of perpendicular line = 8/3

4)
x = -7, slope is undefined
so slope of perpendicular line is 0

5)
3x+2y = 12
2y = -3x + 12
y = -3/2(x) + 6 ; slope = -3/2

5x - 6y = 8
6y = 4x - 8
y = 2/3(x) - 4/3; slope is 2/3

slope is opposite and reciprocal, so the equals are perpendicular

6)
3x + y = 5
y = -3x + 5; slope = -3

6x + 2y = -15
2y = -6x - 15
y = -3x - 7.5; slope = -3

both have slope = -3 so equations are parallel

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3 years ago

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Find the area of the figure. If you need to use Pi in your computation, approximate its value as 3.14. Round to the nearest hund

arsen [322]

Answer:

area of figure= area of rectangle+area of semi-circle

area of rectangle= length ×width

5×4

= 20in²

area of semi circle= 1/2πr²

1/2×22/7×2×2

22×2

44

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3 years ago

Solve for x using figure to the right. Pls answer this it is urgent

goldenfox [79]

Answer:

Therefore the value of x = 10 units

Step-by-step explanation:

Let label the Triangles first,

Δ ABC a right triangle at ∠ A =90°

Δ ADB andΔ ADC a right triangle at ∠ D =90°

Such that

AD = x

BD = 50

CD = 2

∴ BC = BD + DC = 50 + 2 = 52

To Find:

x = ?

Solution:

In right triangle By Pythagoras Theorem,

$(\textrm{Hypotenuse})^{2} = (\textrm{Shorter leg})^{2}+(\textrm{Longer leg})^{2}$

In right triangle Δ ADB andΔ ADC By Pythagoras Theorem we will have,

AB² = BD² + AD²

AB² = 50² + x² ..................equation ( 1 )

and

AC² = DC² + AD²

AC² = 2² + x² ...................equation ( 2 )

Now in right triangle Δ ABC,

BC² = AB² + AC²

Equating equation (1 ) and ( 2 ) and the given value we get

52² = 50² + x² + 2² + x²

∴ 2x² = 2704 - 2504

∴ 2x² =200

∴ $x^{2} =\frac{200}{2}\\\\\therefore x=\pm\sqrt{100} \\\\ \textrm{x cannot be negative}\\\therefore x= 10\ unit$

Therefore the value of x = 10 units

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3 years ago

The height of a box is 7 the length is three inches more than the width find the volume is 126

babunello [35]

Answer:

<h2>answer c: 10</h2>

Step-by-step explanation:

v=H*W*L

280=7*W*(6+W)

280=42W+7W^2

40=6w+w^2

W^2+6W-40=0

(W-4)(W+10)=0

W=4

We can only use positive results

L=6+W

L=4+6=10

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6 0

3 years ago

Simplify the rational expression.

Vadim26 [7]

Answer:

$\frac{x-6}{x-9}$

Step-by-step explanation:

Given

$\frac{x^2-2x-24}{x^2-5x-36}$ ← factor the numerator and denominator

= $\frac{(x-6)(x+4)}{(x-9)(x+4)}$ ← cancel (x + 4 ) on numerator/ denominator

= $\frac{x-6}{x-9}$

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3 years ago